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Hawking radiation is black body radiation that is predicted to be released by black holes, due to quantum effects near the event horizon.

It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974,^[1] and sometimes also after Jacob Bekenstein, who predicted that black holes should have a finite, non-zero temperature and entropy.^[2]

Hawking's work followed his visit to Moscow in 1973 where the Soviet scientists Yakov Zeldovich and Alexei Starobinsky showed him that according to the quantum mechanical uncertainty principle, rotating black holes should create and emit particles.^[3] Hawking radiation reduces the mass and the energy of the black hole and is therefore also known as black hole evaporation. Because of this, black holes that lose more mass than they gain through other means are expected to shrink and ultimately vanish. Micro black holes (MBHs) are predicted to be larger net emitters of radiation than larger black holes and should shrink and dissipate faster.

In September 2010, a signal that is closely related to black hole Hawking radiation (see analog gravity) was claimed to have been observed in a laboratory experiment involving optical light pulses. However, the results remain unverified and debatable.^[4]^[5] Other projects have been launched to look for this radiation within the framework of analog gravity. In June 2008, NASA launched the Fermi space telescope, which will search for the terminal gamma-ray flashes expected from evaporating primordial black holes. In the event that speculative large extra dimension theories are correct, CERN's Large Hadron Collider may be able to create micro black holes and observe their evaporation.^[6]^[7]^[8]^[9]^[10]

Overview

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Black holes are sites of immense gravitational attraction. Classically, the gravitation is so powerful that nothing, not even electromagnetic radiation (including light), can escape from the black hole. It is yet unknown how gravity can be incorporated into quantum mechanics, nevertheless, far from the black hole the gravitational effects can be weak enough for calculations to be reliably performed in the framework of quantum field theory in curved spacetime. Hawking showed that quantum effects allow black holes to emit exact black body radiation, which is the average thermal radiation emitted by an idealized thermal source known as a black body. The electromagnetic radiation is as if it were emitted by a black body with a temperature that is inversely proportional to the black hole's mass.

Physical insight into the process may be gained by imagining that particle-antiparticle radiation is emitted from just beyond the event horizon. This radiation does not come directly from the black hole itself, but rather is a result of virtual particles being "boosted" by the black hole's gravitation into becoming real particles.^[11] As the particle-antiparticle pair was produced by the black hole's gravitational energy, the escape of one of the particles takes away some of the mass of the black hole.^[12]

A slightly more precise, but still much simplified, view of the process is that vacuum fluctuations cause a particle-antiparticle pair to appear close to the event horizon of a black hole. One of the pair falls into the black hole while the other escapes. In order to preserve total energy, the particle that fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole). By this process, the black hole loses mass, and, to an outside observer, it would appear that the black hole has just emitted a particle. In another model, the process is a quantum tunnelling effect, whereby particle-antiparticle pairs will form from the vacuum, and one will tunnel outside the event horizon.^[11]

An important difference between the black hole radiation as computed by Hawking and thermal radiation emitted from a black body is that the latter is statistical in nature, and only its average satisfies what is known as Planck's law of black body radiation, while the former fits the data better. Thus thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and charge of the black hole (the no-hair theorem). This leads to the black hole information paradox.

However, according to the conjectured gauge-gravity duality (also known as the AdS/CFT correspondence), black holes in certain cases (and perhaps in general) are equivalent to solutions of quantum field theory at a non-zero temperature. This means that no information loss is expected in black holes (since no such loss exists in the quantum field theory), and the radiation emitted by a black hole is probably the usual thermal radiation. If this is correct, then Hawking's original calculation should be corrected, though it is not known how (see below).

A black hole of one solar mass has a temperature of only 60 nanokelvin (60 billionths of a kelvin); in fact, such a black hole would absorb far more cosmic microwave background radiation than it emits. A black hole of 4.5 × 10²² kg (about the mass of the Moon) would be in equilibrium at 2.7 kelvin, absorbing as much radiation as it emits. Yet smaller primordial black holes would emit more than they absorb, and thereby lose mass.^[11]

Trans-Planckian problem

The trans-Planckian problem is the observation that Hawking's original calculation requires talking about quantum particles in which the wavelength becomes shorter than the Planck length near the black hole's horizon. It is due to the peculiar behavior near a gravitational horizon where time stops as measured from far away. A particle emitted from a black hole with a finite frequency, if traced back to the horizon, must have had an infinite frequency there and a trans-Planckian wavelength.

The Unruh effect and the Hawking effect both talk about field modes in the superficially stationary space-time that change frequency relative to other coordinates which are regular across the horizon. This is necessarily so, since to stay outside a horizon requires acceleration which constantly Doppler shifts the modes.

An outgoing Hawking radiated photon, if the mode is traced back in time, has a frequency which diverges from that which it has at great distance, as it gets closer to the horizon, which requires the wavelength of the photon to "scrunch up" infinitely at the horizon of the black hole. In a maximally extended external Schwarzschild solution, that photon's frequency only stays regular if the mode is extended back into the past region where no observer can go. That region doesn't seem to be observable and is physically suspect, so Hawking used a black hole solution without a past region which forms at a finite time in the past. In that case, the source of all the outgoing photons can be identified–it is a microscopic point right at the moment that the black hole first formed.

The quantum fluctuations at that tiny point, in Hawking's original calculation, contain all the outgoing radiation. The modes that eventually contain the outgoing radiation at long times are redshifted by such a huge amount by their long sojourn next to the event horizon, that they start off as modes with a wavelength much shorter than the Planck length. Since the laws of physics at such short distances are unknown, some find Hawking's original calculation unconvincing.^[13]^[14]^[15]^[16]^[17]^[18]

The trans-Planckian problem is nowadays mostly considered a mathematical artifact of horizon calculations.^[16]^[19] The same effect occurs for regular matter falling onto a white hole solution. Matter which falls on the white hole accumulates on it, but has no future region into which it can go. Tracing the future of this matter, it is compressed onto the final singular endpoint of the white hole evolution, into a trans-Planckian region. The reason for these types of divergences is that modes which end at the horizon from the point of view of outside coordinates are singular in frequency there. The only way to determine what happens classically is to extend in some other coordinates that cross the horizon.

There exist alternative physical pictures which give the Hawking radiation in which the trans-Planckian problem is addressed. The key point is that similar trans-Planckian problems occur when the modes occupied with Unruh radiation are traced back in time.^[20] In the Unruh effect, the magnitude of the temperature can be calculated from ordinary Minkowski field theory, and is not controversial.

Emission process

Hawking radiation is required by the Unruh effect and the equivalence principle applied to black hole horizons. Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing Hawking radiation.^[20]

A Schwarzschild black hole has a metric

ds^{2}=-\left(1-{2M \over r}\right)dt^{2}+{1 \over 1-2M/r}dr^{2}+r^{2}d\Omega ^{2}.

The black hole is the background spacetime for a quantum field theory.

The field theory is defined by a local path integral, so if the boundary conditions at the horizon are determined, the state of the field outside will be specified. To find the appropriate boundary conditions, consider a stationary observer just outside the horizon at position $r=2M+u^{2}/2M$ . The local metric to lowest order is

ds^{2}=-{u^{2} \over 4M^{2}}dt^{2}+4du^{2}+dX_{\perp }^{2}=-\rho ^{2}d\tau ^{2}+d\rho ^{2}+dX_{\perp }^{2},

which is Rindler in terms of $\tau =t/4M$ and $\rho =2u$ . The metric describes a frame that is accelerating to keep from falling into the black hole. The local acceleration diverges as $u\rightarrow 0$ .

The horizon is not a special boundary, and objects can fall in. So the local observer should feel accelerated in ordinary Minkowski space by the principle of equivalence. The near-horizon observer must see the field excited at a local inverse temperature

\beta (u)=2\pi \rho =(4\pi )u=4\pi {\sqrt {2M(r-2M)}};

this is the Unruh effect.

The gravitational redshift is by the square root of the time component of the metric. So for the field theory state to consistently extend, there must be a thermal background everywhere with the local temperature redshift-matched to the near horizon temperature:

\beta (r')=4\pi {\sqrt {2M(r-2M)}}{\sqrt {1-2M/r' \over 1-2M/r}}.

The inverse temperature redshifted to r' at infinity is

\beta (\infty )=(4\pi ){\sqrt {2Mr}}\;

and $r$ is the near-horizon position, near $2M$ , so this is really

\beta =8\pi M.

So a field theory defined on a black hole background is in a thermal state whose temperature at infinity is

T_{H}={1 \over 8\pi M}.

This can be expressed more cleanly in terms of the surface gravity of the black hole; this is the parameter that determines the acceleration of a near-horizon observer. In natural units ( $G=c=\hbar =k_{\text{B}}=1$ ), the temperature is

T_{H}={\frac {\kappa }{2\pi }},

where $\kappa$ is the surface gravity of the horizon. So a black hole can only be in equilibrium with a gas of radiation at a finite temperature. Since radiation incident on the black hole is absorbed, the black hole must emit an equal amount to maintain detailed balance. The black hole acts as a perfect blackbody radiating at this temperature.

In SI units, the radiation from a Schwarzschild black hole is black-body radiation with temperature

T={\hbar \,c^{3} \over 8\pi GMk_{\text{B}}}\;\quad \left(\approx {1.227\times 10^{23}\;{\text{kg}} \over M}\;{\text{K}}\right),

where $\hbar$ is the reduced Planck constant, c is the speed of light, k_B is the Boltzmann constant, G is the gravitational constant, and M is the mass of the black hole.

From the black hole temperature, it is straightforward to calculate the black hole entropy. The change in entropy when a quantity of heat dQ is added is

dS={dQ \over T}=8\pi MdQ.

The heat energy that enters serves to increase the total mass, so

dS=8\pi MdM=d(4\pi M^{2}).

.

The radius of a black hole is twice its mass in natural units, so the entropy of a black hole is proportional to its surface area:

S=\pi R^{2}={A \over 4}.

Assuming that a small black hole has zero entropy, the integration constant is zero. Forming a black hole is the most efficient way to compress mass into a region, and this entropy is also a bound on the information content of any sphere in space time. The form of the result strongly suggests that the physical description of a gravitating theory can be somehow encoded onto a bounding surface.

Black hole evaporation

When particles escape, the black hole loses a small amount of its energy and therefore some of its mass (mass and energy are related by Einstein's equation E = mc²).

The power emitted by a black hole in the form of Hawking radiation can easily be estimated for the simplest case of a nonrotating, non-charged Schwarzschild black hole of mass $M$ . Combining the formulas for the Schwarzschild radius of the black hole, the Stefan–Boltzmann law of black-body radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a sphere (the black hole's event horizon), equation derivation:

Stefan–Boltzmann constant:

\sigma ={\frac {\pi ^{2}k_{B}^{4}}{60\hbar ^{3}c^{2}}}\;

Schwarzschild radius:

r_{s}={\frac {2GM}{c^{2}}}\;

Black hole surface gravity at the horizon:

g={\frac {GM}{r_{s}^{2}}}={\frac {c^{4}}{4GM}}\;

Hawking radiation has a black-body (Planck) spectrum with a temperature T given by:

E=k_{B}T={\frac {\hbar g}{2\pi c}}={\frac {\hbar }{2\pi c}}\left({\frac {c^{4}}{4GM}}\right)={\frac {\hbar c^{3}}{8\pi GM}}\;

Hawking radiation temperature:

T_{H}={\frac {\hbar c^{3}}{8\pi GMk_{B}}}\;

Schwarzschild sphere surface area of Schwarzschild radius $r_{s}$ :

A_{s}=4\pi r_{s}^{2}=4\pi \left({\frac {2GM}{c^{2}}}\right)^{2}={\frac {16\pi G^{2}M^{2}}{c^{4}}}\;

Stefan–Boltzmann power law:

P=A_{s}j^{\star }=A_{s}\epsilon \sigma T^{4}\;

A black hole is a perfect black-body:

\epsilon =1\;

Stefan–Boltzmann–Schwarzschild–Hawking black hole radiation power law derivation:

P=A_{s}\epsilon \sigma T_{H}^{4}=\left({\frac {16\pi G^{2}M^{2}}{c^{4}}}\right)\left({\frac {\pi ^{2}k_{B}^{4}}{60\hbar ^{3}c^{2}}}\right)\left({\frac {\hbar c^{3}}{8\pi GMk_{B}}}\right)^{4}={\frac {\hbar c^{6}}{15360\pi G^{2}M^{2}}}\;

Stefan–Boltzmann-Schwarzschild-Hawking power law:

P={\frac {\hbar c^{6}}{15360\pi G^{2}M^{2}}}\;

Where $P$ is the energy outflow, $\hbar$ is the reduced Planck constant, $c$ is the speed of light, and $G$ is the gravitational constant. It is worth mentioning that the above formula has not yet been derived in the framework of semiclassical gravity.

The power in the Hawking radiation from a solar mass ( $M_{\odot }$ ) black hole turns out to be a minuscule 9 × 10⁻²⁹ watts. It is indeed an extremely good approximation to call such an object 'black'.

P={\frac {\hbar c^{6}}{15360\pi G^{2}M_{\odot }^{2}}}=9.004\times 10^{-29}\;{\text{W}}\;

Under the assumption of an otherwise empty universe, so that no matter or cosmic microwave background radiation falls into the black hole, it is possible to calculate how long it would take for the black hole to dissipate:

K_{\operatorname {ev} }={\frac {\hbar c^{6}}{15360\pi G^{2}}}=3.562\times 10^{32}\;{\text{W}}\cdot {\text{kg}}^{2}\;

Given that the power of the Hawking radiation is the rate of evaporation energy loss of the black hole:

P=-{\frac {dE}{dt}}={\frac {K_{\operatorname {ev} }}{M^{2}}}\;

Since the total energy E of the black hole is related to its mass M by Einstein's mass-energy formula:

E=Mc^{2}\;

P=-{\frac {dE}{dt}}=-\left({\frac {d}{dt}}\right)Mc^{2}=-c^{2}{\frac {dM}{dt}}\;

We can then equate this to our above expression for the power:

-c^{2}{\frac {dM}{dt}}={\frac {K_{\operatorname {ev} }}{M^{2}}}\;

This differential equation is separable, and we can write:

M^{2}dM=-{\frac {K_{\operatorname {ev} }}{c^{2}}}dt\;

The black hole's mass is now a function M(t) of time t. Integrating over M from $M_{0}$ (the initial mass of the black hole) to zero (complete evaporation), and over t from zero to $t_{\operatorname {ev} }\;$ :

\int _{M_{0}}^{0}M^{2}dM=-{\frac {K_{\operatorname {ev} }}{c^{2}}}\int _{0}^{t_{\operatorname {ev} }}dt\;

The evaporation time of a black hole is proportional to the cube of its mass:

t_{\operatorname {ev} }={\frac {c^{2}M_{0}^{3}}{3K_{\operatorname {ev} }}}=\left({\frac {c^{2}M_{0}^{3}}{3}}\right)\left({\frac {15360\pi G^{2}}{\hbar c^{6}}}\right)={\frac {5120\pi G^{2}M_{0}^{3}}{\hbar c^{4}}}=8.410\times 10^{-17}\left[{\frac {M_{0}}{\mathrm {kg} }}\right]^{3}\mathrm {s} \;

The time that the black hole takes to dissipate is:

t_{\operatorname {ev} }={\frac {5120\pi G^{2}M_{0}^{3}}{\hbar c^{4}}}\;

Where $M_{0}$ is the mass of the black hole.

The lower classical quantum limit for mass for this equation is equivalent to the Planck mass, $m_{P}$ .

Planck mass quantum black hole Hawking radiation evaporation time:

t_{\operatorname {ev} }={\frac {5120\pi G^{2}m_{P}^{3}}{\hbar c^{4}}}=5120\pi t_{P}=5120\pi {\sqrt {\frac {\hbar G}{c^{5}}}}=8.671\times 10^{-40}\;{\text{s}}\;

t_{\operatorname {ev} }=5120\pi {\sqrt {\frac {\hbar G}{c^{5}}}}\;

Where $t_{P}$ is the Planck time.

For a black hole of one solar mass ( $M_{\odot }$ = 1.98892 × 10³⁰ kg), we get an evaporation time of 2.098 × 10⁶⁷ years—much longer than the current age of the universe at 13.798 ± 0.037 x 10⁹years.^[21]

t_{\operatorname {ev} }={\frac {5120\pi G^{2}M_{\odot }^{3}}{\hbar c^{4}}}=6.617\times 10^{74}\;{\text{s}}\;

But for a black hole of 10¹¹ kg, the evaporation time is 2.667 billion years. This is why some astronomers are searching for signs of exploding primordial black holes.

However, since the universe contains the cosmic microwave background radiation, in order for the black hole to dissipate, it must have a temperature greater than that of the present-day black-body radiation of the universe of 2.7 K = 2.3 × 10⁻⁴ eV. This implies that $M$ must be less than 0.8 of the mass of the Earth^[22] - approximately the mass of the Moon.

Cosmic microwave background radiation universe temperature:

T_{u}=2.725\;{\text{K}}\;

Hawking total black hole mass:

M_{H}\leq {\frac {\hbar c^{3}}{8\pi Gk_{B}T_{u}}}\leq 4.503\times 10^{22}\;{\text{kg}}\;

M_{H}\leq {\frac {\hbar c^{3}}{8\pi Gk_{B}T_{u}}}\;

{\frac {M_{H}}{M_{\oplus }}}=7.539\times 10^{-3}=0.754\;\%\;

Where, $M_{\oplus }$ is the total Earth mass.

In common units,

P=3.563\,45\times 10^{32}\left[{\frac {\mathrm {kg} }{M}}\right]^{2}\mathrm {W} \;

t_{\mathrm {ev} }=8.407\,16\times 10^{-17}\left[{\frac {M_{0}}{\mathrm {kg} }}\right]^{3}\mathrm {s} \ \ \approx \ 2.66\times 10^{-24}\left[{\frac {M_{0}}{\mathrm {kg} }}\right]^{3}\mathrm {yr} \;

M_{0}=2.282\,71\times 10^{5}\left[{\frac {t_{\mathrm {ev} }}{\mathrm {s} }}\right]^{1/3}\mathrm {kg} \ \ \approx \ 7.2\times 10^{7}\left[{\frac {t_{\mathrm {ev} }}{\mathrm {yr} }}\right]^{1/3}\mathrm {kg} \;

So, for instance, a 1-second-lived black hole has a mass of 2.28 × 10⁵ kg, equivalent to an energy of 2.05 × 10²² J that could be released by 5 × 10⁶ megatons of TNT. The initial power is 6.84 × 10²¹ W.

Black hole evaporation has several significant consequences:

Black hole evaporation produces a more consistent view of black hole thermodynamics, by showing how black holes interact thermally with the rest of the universe.
Unlike most objects, a black hole's temperature increases as it radiates away mass. The rate of temperature increase is exponential, with the most likely endpoint being the dissolution of the black hole in a violent burst of gamma rays. A complete description of this dissolution requires a model of quantum gravity, however, as it occurs when the black hole approaches Planck mass and Planck radius.
The simplest models of black hole evaporation lead to the black hole information paradox. The information content of a black hole appears to be lost when it dissipates, as under these models the Hawking radiation is random (it has no relation to the original information). A number of solutions to this problem have been proposed, including suggestions that Hawking radiation is perturbed to contain the missing information, that the Hawking evaporation leaves some form of remnant particle containing the missing information, and that information is allowed to be lost under these conditions.

Large extra dimensions

Formulae from the previous section are only applicable if laws of gravity are approximately valid all the way down to the Planck scale. In particular, for black holes with masses below Planck mass (~10⁻⁵ g), they result in unphysical lifetimes below Planck time (~10⁻⁴³ s). This is normally seen as an indication that Planck mass is the lower limit on the mass of a black hole.

In the model with large extra dimensions, values of Planck constants can be radically different, and formulas for Hawking radiation have to be modified as well. In particular, the lifetime of a micro black hole (with radius below the scale of extra dimensions) is given by

\tau \sim {1 \over M_{*}}{\Bigl (}{M_{BH} \over M_{*}}{\Bigr )}^{(n+3)/(n+1)}

where $M_{*}$ is the low energy scale (which could be as low as a few TeV), and n is the number of large extra dimensions. This formula is now consistent with black holes as light as a few TeV, with lifetimes on the order of "new Planck time" ~10⁻²⁶ s.

Experimental observation of Hawking radiation

Under experimentally achievable conditions for gravitational systems this effect is too small to be observed directly. In September 2010, however, an experimental set-up created a laboratory "white hole event horizon" that the experimenters claimed was shown to radiate Hawking radiation,^[23] although its status as a genuine confirmation remains in doubt.^[24] Some scientists predict that Hawking radiation could be studied by analogy using sonic black holes, in which sound perturbations are analogous to light in a gravitational black hole and the flow of an approximately perfect fluid is analogous to gravity.^[25]

Notes

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The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang → first detailed studies of the evaporation mechanism
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang → links between primordial black holes and the early universe
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang → experimental searches for primordial black holes thanks to the emitted antimatter
Template:Cite arXiv → cosmology with primordial black holes
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang → searches for new physics (quantum gravity) with primordial black holes
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang → evaporating black holes and extra-dimensions
D. Ida, K.-y. Oda & S.C.Park, Phys. Rev. D67 (2003) 064025,Phys. Rev. D71 (2005) 124039,[1]: determination of black hole's life and extra-dimensions
N. Nicolaevici, J. Phys. A: Math. Gen. 36 (2003) 7667-7677 [2]: consistent derivation of the Hawking radiation in the Fulling-Davies mirror model.
L. Smolin, Quantum gravity faces reality, consists of the recent developments and predictions of loop quantum gravity about gravity in small scales including the deviation from Hawking radiation effect by Ansari Spectroscopy of a canonically quantized horizon.
M. Ansari, Area, ladder symmetry, degeneracy and fluctuations of a horizon studies the deviation of a loop quantized black hole from Hawking radiation. A novel observable quantum effect of black hole quantization is introduced.
Stuart L. Shapiro, Saul A. Teukolsky (1983), Black holes, white dwarfs, and neutron stars: The physics of compact objects. p. 366 Wiley-Interscience, Hawking radiation evaporation formula derivation.
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

External links

Hawking radiation calculator tool
The case for mini black holes A. Barrau & J. Grain explain how the Hawking radiation could be detected at colliders
University of Colorado at Boulder
Hawking radiation on arxiv.org
Hawking radiation observed in laboratory?

Template:Quantum gravity Template:Stephen Hawking

↑ Charlie Rose: A conversation with Dr. Stephen Hawking & Lucy Hawking
↑ Template:Cite news
↑ A Brief History of Time, Stephen Hawking, Bantam Books, 1988.
↑ Hawking radiation from ultrashort laser pulse filaments Authors: F. Belgiorno, S.L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V.G. Sala, D. Faccio http://arxiv.org/abs/1009.4634
↑ Template:Cite web
↑ S.B. Giddings and S.D. Thomas, "High-energy colliders as black hole factories: The End of short distance physics," arXiv:hep-ph/0106219, Phys. Rev. D65:056010 (2002).
↑ S. Dimopoulos and G.L. Landsberg, "Black holes at the LHC", arXiv:hep-ph/0106295, Phys. Rev. Lett. 87:161602 (2001)
↑ Template:Cite web
↑ American Institute of Physics Bulletin of Physics News, Number 558, September 26, 2001, by Phillip F. Schewe, Ben Stein, and James Riordon
↑ Template:Cite news
↑ ^11.0 ^11.1 ^11.2 Template:Cite doi
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Adam D. Helfer: Do black holes radiate?
↑ G. 't Hooft, Nuclear Phys B256, 727 (1985)
↑ T. Jacobson, Phys Review D 44 1731 (1991)
↑ ^16.0 ^16.1 http://www.fys.ruu.nl/~wwwthe/lectures/itfuu-0196.ps (p.46)
↑ R. Brout, S. Massar, R. Parentani, Ph. Spindel, Hawking radiation without trans-Planckian frequencies, Phys. Rev. D 52, 4559 - 4568 (1995)
↑ Helfer, Adam D. Trans-Planckian Modes, Back-Reaction, and the Hawking Process, http://arxiv.org/abs/gr-qc/0008016
↑ Analog Gravity
↑ ^20.0 ^20.1 For an alternative derivation and more detailed discussion of Hawking radiation as a form of Unruh radiation see Bryce de Witt's chapter Quantum gravity: the new synthesis pg c.696 in General Relativity: An Einstein Centenary eds S Hawking and W Israel, ISBN 0-521-29928-4
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ [astro-ph/9911309] The Last Eight Minutes of a Primordial Black Hole
↑ "First Observation of Hawking Radiation" from the Technology Review
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ C. Barceló, S. Liberati and M. Visser, “Towards the observation of Hawking radiation in Bose–Einstein condensates,” arXiv:gr-qc/0110036 Int. J. Mod. Phys. A 18, 3735 (2003) .

[1] Charlie Rose: A conversation with Dr. Stephen Hawking & Lucy Hawking

[2] Template:Cite news

[3] A Brief History of Time, Stephen Hawking, Bantam Books, 1988.

[Milanoguys-4] Hawking radiation from ultrashort laser pulse filaments Authors: F. Belgiorno, S.L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V.G. Sala, D. Faccio http://arxiv.org/abs/1009.4634

[5] Template:Cite web

[6] S.B. Giddings and S.D. Thomas, "High-energy colliders as black hole factories: The End of short distance physics," arXiv:hep-ph/0106219, Phys. Rev. D65:056010 (2002).

[7] S. Dimopoulos and G.L. Landsberg, "Black holes at the LHC", arXiv:hep-ph/0106295, Phys. Rev. Lett. 87:161602 (2001)

[courier-8] Template:Cite web

[9] American Institute of Physics Bulletin of Physics News, Number 558, September 26, 2001, by Phillip F. Schewe, Ben Stein, and James Riordon

[10] Template:Cite news

[kumar2012-11] 11.0 ^11.1 ^11.2 Template:Cite doi

[12] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[13] Adam D. Helfer: Do black holes radiate?

[14] G. 't Hooft, Nuclear Phys B256, 727 (1985)

[15] T. Jacobson, Phys Review D 44 1731 (1991)

[autogenerated1-16] 16.0 ^16.1 http://www.fys.ruu.nl/~wwwthe/lectures/itfuu-0196.ps (p.46)

[17] R. Brout, S. Massar, R. Parentani, Ph. Spindel, Hawking radiation without trans-Planckian frequencies, Phys. Rev. D 52, 4559 - 4568 (1995)

[18] Helfer, Adam D. Trans-Planckian Modes, Back-Reaction, and the Hawking Process, http://arxiv.org/abs/gr-qc/0008016

[19] Analog Gravity

[witt-blah-20] 20.0 ^20.1 For an alternative derivation and more detailed discussion of Hawking radiation as a form of Unruh radiation see Bryce de Witt's chapter Quantum gravity: the new synthesis pg c.696 in General Relativity: An Einstein Centenary eds S Hawking and W Israel, ISBN 0-521-29928-4

[planck_cosmological_parameters-21] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[22] [astro-ph/9911309] The Last Eight Minutes of a Primordial Black Hole

[23] "First Observation of Hawking Radiation" from the Technology Review

[24] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[25] C. Barceló, S. Liberati and M. Visser, “Towards the observation of Hawking radiation in Bose–Einstein condensates,” arXiv:gr-qc/0110036 Int. J. Mod. Phys. A 18, 3735 (2003) .

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Revision as of 15:46, 31 January 2014

Contents

Overview

Trans-Planckian problem

Emission process

Black hole evaporation

Large extra dimensions

Experimental observation of Hawking radiation

See also

Notes

Further reading

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+[[File:BlackHole.jpg|thumb|Artist's depiction of a [[black hole]]]]
+'''Hawking radiation''' is [[black body radiation]] that is predicted to be released by [[black hole]]s, due to [[quantum physics|quantum]] effects near the [[event horizon]].
+It is named after the physicist [[Stephen Hawking]], who provided a theoretical argument for its existence in 1974,<ref>[http://www.charlierose.com/guest/view/6294 Charlie Rose: A conversation with Dr. Stephen Hawking & Lucy Hawking]</ref> and sometimes also after [[Jacob Bekenstein]], who predicted that black holes should have a finite, non-zero [[temperature]] and [[entropy]].<ref>{{cite news|last=Levi Julian|first=Hana|title='40 Years of Black Hole Thermodynamics' in Jerusalem|url=http://www.israelnationalnews.com/News/News.aspx/159585#.UErd_yJipNs|accessdate=8 September 2012|newspaper=[[Arutz Sheva]]|date=3 September 2012}}</ref>
+Hawking's work followed his visit to [[Moscow]] in 1973 where the Soviet scientists [[Yakov Zeldovich]] and Alexei Starobinsky showed him that according to the quantum mechanical [[uncertainty principle]], [[rotating black hole]]s should create and emit particles.<ref>''A Brief History of Time'', Stephen Hawking, Bantam Books, 1988.</ref> Hawking radiation reduces the mass and the energy of the black hole and is therefore also known as ''black hole evaporation''. Because of this, black holes that lose more mass than they gain through other means are expected to shrink and ultimately vanish. [[Micro black hole]]s (MBHs) are predicted to be larger net emitters of radiation than larger black holes and should shrink and dissipate faster.
+In September 2010, a signal that is closely related to black hole Hawking radiation (see [[Analog models of gravity|analog gravity]]) was claimed to have been observed in a laboratory experiment involving optical light pulses. However, the results remain unverified and debatable.<ref name="Milanoguys">Hawking radiation from ultrashort laser pulse filaments
+Authors: F. Belgiorno, S.L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V.G. Sala, D. Faccio http://arxiv.org/abs/1009.4634</ref><ref>{{cite web|title=Ultrafast Laser Pulse Makes Desktop Black Hole Glow|work=[[Wired (magazine)|Wired]]|date=29 September 2010|author=Lisa Grossman|url=http://www.wired.com/wiredscience/2010/09/hawking-radiation-in-the-lab/|accessdate=30 April 2012}}</ref> Other projects have been launched to look for this radiation within the framework of [[Analog models of gravity|analog gravity]]. In June 2008, [[NASA]] launched the [[Fermi Gamma-ray Space Telescope|Fermi space telescope]], which will search for the terminal gamma-ray flashes expected from evaporating [[primordial black hole]]s. In the event that speculative [[large extra dimension]] theories are correct, [[CERN|CERN's]] [[Large Hadron Collider]] may be able to create micro black holes and observe their evaporation.<ref>S.B. Giddings and S.D. Thomas, "High-energy colliders as black hole factories: The End of short distance physics," [http://arXiv.org/abs/hep-ph/0106219 arXiv:hep-ph/0106219], [http://prola.aps.org/abstract/PRD/v65/i5/e056010 Phys. Rev. D65:056010 (2002)].</ref><ref>S. Dimopoulos and G.L. Landsberg, "Black holes at the LHC", [http://arxiv.org/abs/hep-ph/0106295 arXiv:hep-ph/0106295],
+[http://prola.aps.org/abstract/PRL/v87/i16/e161602 Phys. Rev. Lett. 87:161602 (2001)]</ref><ref name="courier">{{cite web|url=http://cerncourier.com/cws/article/cern/29199|title=CERN courier - ''The case for mini black holes. Nov 2004''}}</ref><ref>American Institute of Physics Bulletin of Physics News, Number 558, September 26, 2001, by Phillip F. Schewe, Ben Stein, and James Riordon</ref><ref>{{cite news| url=http://www.timesonline.co.uk/tol/news/uk/science/article4715761.ece | work=The Times | location=London | title=Stephen Hawkings 50 bet on the world the universe and the God particle | first=Mark | last=Henderson | date=September 9, 2008 | accessdate=May 4, 2010}}</ref>
+==Overview==
+{{general relativity}}
+[[Black holes]] are sites of immense [[gravity|gravitational attraction]]. Classically, the gravitation is so powerful that nothing, not even [[electromagnetic radiation]] (including [[light]]), can escape from the black hole. It is yet unknown how [[gravity]] can be incorporated into [[quantum mechanics]], nevertheless, far from the black hole the gravitational effects can be weak enough for calculations to be reliably performed in the framework of [[quantum field theory in curved spacetime]]. Hawking showed that quantum effects allow [[black holes]] to emit exact [[black body radiation]], which is the average thermal radiation emitted by an idealized thermal source known as a black body. The [[electromagnetic radiation]] is as if it were emitted by a black body with a [[temperature]] that is [[proportionality (mathematics)|inversely proportional]] to the black hole's [[mass]].
+Physical insight into the process may be gained by imagining that [[elementary particle|particle]]-[[antiparticle]] radiation is emitted from just beyond the [[event horizon]]. This radiation does not come directly from the black hole itself, but rather is a result of [[virtual particle]]s being "boosted" by the black hole's gravitation into becoming real particles.<ref name="kumar2012">{{cite doi|10.3968/j.ans.1715787020120502.1817}}</ref> As the particle-antiparticle pair was produced by the black hole's gravitational energy, the escape of one of the particles takes away some of the mass of the black hole.<ref>{{Citation
+  | last = Carroll
+  | first = Bradley
+  | coauthors = Dale Ostlie
+  | pages = 673
+  | title = An Introduction to Modern Astrophysics
+  | publisher = Addison Wesley
+  | year = 1996
+  | isbn = 0-201-54730-9 }}</ref>
+A slightly more precise, but still much simplified, view of the process is that [[vacuum fluctuation]]s cause a particle-antiparticle pair to appear close to the event horizon of a black hole. One of the pair falls into the black hole while the other escapes. In order to preserve total [[energy]], the particle that fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole). By this process, the black hole loses mass, and, to an outside observer, it would appear that the black hole has just emitted a [[Elementary particle|particle]].  In another model, the process is a [[quantum tunnelling]] effect, whereby particle-antiparticle pairs will form from the vacuum, and one will tunnel outside the event horizon.<ref name="kumar2012"/>
+An important difference between the black hole [[radiation]] as computed by Hawking and [[thermal radiation]] emitted from a black body is that the latter is statistical in nature, and only its average satisfies what is known as [[Planck's law of black body radiation]], while the former fits the data better. Thus [[thermal radiation]] contains [[information]] about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the [[mass]], [[angular momentum]], and [[Charge (physics)|charge]] of the black hole (the [[no-hair theorem]]). This leads to the [[black hole information paradox]].
+However, according to the conjectured [[String theory#Gauge-gravity duality|gauge-gravity duality]] (also known as the [[AdS/CFT correspondence]]), black holes in certain cases (and perhaps in general) are equivalent to solutions of [[quantum field theory]] at a non-zero [[temperature]]. This means that no information loss is expected in black holes (since no such loss exists in the [[quantum field theory]]), and the radiation emitted by a black hole is probably the usual thermal radiation. If this is correct, then Hawking's original calculation should be corrected, though it is not known how (see [[Hawking radiation#Trans-Planckian problem|below]]).
+A black hole of one [[solar mass]] has a temperature of only 60 nanokelvin (60 [[nano-|billionths]] of a [[kelvin]]); in fact, such a black hole would absorb far more [[cosmic microwave background radiation]] than it emits. A black hole of 4.5&nbsp;×&nbsp;10<sup>22</sup>&nbsp;kg (about the mass of the [[Moon]]) would be in equilibrium at 2.7 kelvin, absorbing as much radiation as it emits. Yet smaller [[primordial black hole]]s would emit more than they absorb, and thereby lose mass.<ref name="kumar2012"/>
+== Trans-Planckian problem ==
+The [[trans-Planckian problem]] is the observation that Hawking's original calculation requires talking about [[quantum]] particles in which the [[wavelength]] becomes shorter than the [[Planck length]] near the black hole's horizon. It is due to the peculiar behavior near a gravitational horizon where time stops as measured from far away. A particle emitted from a black hole with a [[Wikt:finite|finite]] [[frequency]], if traced back to the horizon, must have had an [[Infinity|infinite]] frequency there and a trans-Planckian wavelength.
+The [[Unruh effect]] and the Hawking effect both talk about field modes in the superficially stationary [[space-time]] that change frequency relative to other coordinates which are regular across the horizon. This is necessarily so, since to stay outside a horizon requires acceleration which constantly [[Doppler shift]]s the modes.
+An outgoing Hawking radiated [[photon]], if the mode is traced back in time, has a frequency which diverges from that which it has at great distance, as it gets closer to the horizon, which requires the wavelength of the photon to "scrunch up" infinitely at the horizon of the black hole. In a maximally extended external [[Schwarzschild metric|Schwarzschild solution]], that photon's frequency only stays regular if the mode is extended back into the past region where no observer can go. That region doesn't seem to be observable and is physically suspect, so Hawking used a black hole solution without a past region which forms at a finite time in the past. In that case, the source of all the outgoing photons can be identified–it is a microscopic point right at the moment that the black hole first formed.
+The [[quantum]] fluctuations at that tiny point, in Hawking's original calculation, contain all the outgoing radiation. The modes that eventually contain the outgoing radiation at long times are redshifted by such a huge amount by their long sojourn next to the event horizon, that they start off as modes with a wavelength much shorter than the Planck length. Since the laws of physics at such short distances are unknown, some find Hawking's original calculation unconvincing.<ref>[http://arxiv.org/abs/gr-qc/0304042 Adam D. Helfer: Do black holes radiate?]</ref><ref>G. 't Hooft, Nuclear Phys B256, 727 (1985)</ref><ref>T. Jacobson, Phys Review D 44 1731 (1991)</ref><ref name="autogenerated1">http://www.fys.ruu.nl/~wwwthe/lectures/itfuu-0196.ps  (p.46)</ref><ref>R. Brout, S. Massar, R. Parentani, Ph. Spindel, ''Hawking radiation without trans-Planckian frequencies'', Phys. Rev. D 52, 4559 - 4568 (1995)</ref><ref>Helfer, Adam D. ''Trans-Planckian Modes, Back-Reaction, and the Hawking Process'', http://arxiv.org/abs/gr-qc/0008016</ref>
+The trans-Planckian problem is nowadays mostly considered a mathematical artifact of horizon calculations.<ref name="autogenerated1" /><ref>[http://relativity.livingreviews.org/open?pubNo=lrr-2005-12&amp;page=articlesu11.html Analog Gravity<!-- Bot generated title -->]</ref> The same effect occurs for regular matter falling onto a [[white hole]] solution. Matter which falls on the white hole accumulates on it, but has no future region into which it can go. Tracing the future of this matter, it is compressed onto the final singular endpoint of the white hole evolution, into a trans-Planckian region. The reason for these types of divergences is that modes which end at the horizon from the point of view of outside coordinates are singular in frequency there. The only way to determine what happens classically is to extend in some other coordinates that cross the horizon.
+There exist alternative physical pictures which give the Hawking radiation in which the trans-Planckian problem is addressed. The key point is that similar trans-Planckian problems occur when the modes occupied with Unruh radiation are traced back in time.<ref name="witt-blah">For an alternative derivation and more detailed discussion of Hawking radiation as a form of Unruh radiation see [[Bryce de Witt]]'s chapter ''Quantum gravity: the new synthesis'' pg c.696 in
+''General Relativity: An Einstein Centenary'' eds S Hawking and W Israel, ISBN 0-521-29928-4</ref> In the Unruh effect, the magnitude of the temperature can be calculated from ordinary [[Hermann Minkowski|Minkowski]] field theory, and is not controversial.
+==Emission process==
+Hawking radiation is required by the Unruh effect and the [[equivalence principle]] applied to black hole horizons. Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing Hawking radiation.<ref name="witt-blah"/>
+A [[Schwarzschild black hole]] has a metric
+:<math>
+ds^2 = -\left(1-{2M\over r}\right)dt^2 + {1\over 1- 2M/r} dr^2 + r^2 d\Omega^2.</math>
+The black hole is the background spacetime for a quantum field theory.
+The field theory is defined by a local path integral, so if the boundary conditions at the horizon are determined, the state of the field outside will be specified. To find the appropriate boundary conditions, consider a stationary observer just outside the horizon at position <math>r = 2M + u^2/2M</math>. The local metric to lowest order is
+:<math>
+ds^2 = - {u^2\over 4M^2} dt^2 + 4 du^2 + dX_\perp^2 = - \rho^2 d\tau^2 + d\rho^2 + dX_\perp^2,</math>
+which is [[Rindler coordinates|Rindler]] in terms of <math>\tau=t/4M</math> and <math>\rho=2u</math>. The metric describes a frame that is accelerating to keep from falling into the black hole. The local acceleration diverges as <math>u\rightarrow 0</math>.
+The horizon is not a special boundary, and objects can fall in. So the local observer should feel accelerated in ordinary Minkowski space by the principle of equivalence. The near-horizon observer must see the field excited at a local inverse temperature
+:<math>\beta(u)=2\pi \rho = (4\pi) u = 4\pi \sqrt{2M(r-2M)};</math>
+this is the [[Unruh effect]].
+The gravitational redshift is by the square root of the time component of the metric. So for the field theory state to consistently extend, there must be a thermal background everywhere with the local temperature redshift-matched to the near horizon temperature:
+:<math>\beta(r') = 4\pi \sqrt{2M(r-2M)} \sqrt{1- 2M/r' \over 1- 2M/r}.</math>
+The inverse temperature redshifted to r' at infinity is
+:<math>\beta(\infty) = (4\pi)\sqrt{2Mr} \;</math>
+and <math>r</math> is the near-horizon position, near <math>2M</math>, so this is really
+:<math>\beta = 8 \pi M.</math>
+So a field theory defined on a black hole background is in a thermal state whose temperature at infinity is
+:<math>T_H = {1 \over 8 \pi M}.</math>
+This can be expressed more cleanly in terms of the [[surface gravity]] of the black hole; this is the parameter that determines the acceleration of a near-horizon observer. In [[natural units]] (<math> G = c = \hbar = k_\text{B} = 1</math>), the temperature is
+:<math>T_H = \frac{\kappa}{2 \pi},</math>
+where <math>\kappa</math> is the [[surface gravity]] of the horizon. So a black hole can only be in equilibrium with a gas of radiation at a finite temperature. Since radiation incident on the black hole is absorbed, the black hole must emit an equal amount to maintain [[detailed balance]]. The black hole acts as a [[blackbody radiation|perfect blackbody]] radiating at this temperature.
+In [[SI units]], the radiation from a [[Schwarzschild metric|Schwarzschild]] black hole is [[black-body radiation]] with temperature
+:<math>T = {\hbar \, c^3 \over 8 \pi G M k_\text{B}} \;\quad \left(\approx {1.227 \times 10^{23}\; \text{kg} \over M}\; \text{K} \right),</math>
+where <math>\hbar</math> is the [[Planck's constant|reduced Planck constant]], ''c'' is the [[speed of light]], ''k''<sub>B</sub> is the [[Boltzmann constant]], ''G'' is the [[gravitational constant]], and ''M'' is the [[mass]] of the black hole.
+From the black hole temperature, it is straightforward to calculate the black hole entropy. The change in entropy when a quantity of heat ''dQ'' is added is
+:<math>dS = {dQ\over T} = 8\pi M dQ.</math>
+The heat energy that enters serves to increase the total mass, so
+:<math>dS = 8 \pi M dM = d(4 \pi M^2).</math>.
+The radius of a black hole is twice its mass in [[natural units]], so the entropy of a black hole is proportional to its surface area:
+:<math>S = \pi R^2 = {A \over 4}.</math>
+Assuming that a small black hole has zero entropy, the integration constant is zero. Forming a black hole is the most efficient way to compress mass into a region, and this entropy is also a bound on the information content of any sphere in space time. The form of the result strongly suggests that the physical description of a gravitating theory can be [[holography|somehow encoded]] onto a bounding surface.
+==Black hole evaporation==
+When particles escape, the black hole loses a small amount of its energy and therefore some of its mass (mass and energy are related by [[special relativity|Einstein's equation]]  ''[[E = mc²]]'').
+The [[Power (physics)|power]] emitted by a black hole in the form of Hawking radiation can easily be estimated for the simplest case of a nonrotating, non-charged [[Schwarzschild black hole]] of mass <math>M</math>. Combining the formulas for the [[Schwarzschild radius]] of the black hole, the [[Stefan–Boltzmann law]] of black-body radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a [[sphere]] (the black hole's event horizon), equation derivation:
+[[Stefan–Boltzmann constant]]:
+:<math>\sigma = \frac{\pi^2 k_B^4}{60 \hbar^3 c^2} \;</math>
+[[Schwarzschild radius]]:
+:<math>r_s = \frac{2GM}{c^2} \;</math>
+Black hole [[surface gravity]] at the horizon:
+:<math>g = \frac{G M}{r_s^2} = \frac{c^4}{4 G M} \;</math>
+Hawking radiation has a [[Black-body radiation|black-body]] (Planck) spectrum with a temperature T given by:
+:<math>E = k_B T = \frac{\hbar g}{2 \pi c} = \frac{\hbar}{2 \pi c} \left( \frac{c^4}{4 G M} \right) = \frac{\hbar c^3}{8 \pi G M} \;</math>
+Hawking radiation temperature:
+:{|cellpadding="2" style="border:2px solid #ccccff"
+|<math>T_H = \frac{\hbar c^3}{8 \pi G M k_B} \;</math>
+|}
+Schwarzschild [[sphere]] surface area of [[Schwarzschild radius]] <math>r_s</math>:
+:<math>A_s = 4 \pi r_s^2 = 4 \pi \left( \frac{2 G M}{c^2} \right)^2 = \frac{16 \pi G^2 M^2}{c^4} \;</math>
+[[Stefan–Boltzmann law|Stefan–Boltzmann]] power law:
+:<math>P = A_s j^{\star} = A_s \epsilon \sigma T^{4} \;</math>
+A black hole is a perfect black-body:
+:<math>\epsilon = 1 \;</math>
+Stefan–Boltzmann–Schwarzschild–Hawking black hole radiation power law derivation:
+:<math>P = A_s \epsilon \sigma T_H^4 = \left( \frac{16 \pi G^2 M^2}{c^4} \right) \left( \frac{\pi^2 k_B^4}{60 \hbar^3 c^2} \right) \left( \frac{\hbar c^3}{8 \pi G M k_B} \right)^4 = \frac{\hbar c^6}{15360 \pi G^2 M^2} \;</math>
+Stefan–Boltzmann-Schwarzschild-Hawking power law:
+:{|cellpadding="2" style="border:2px solid #ccccff"
+|<math>P = \frac{\hbar c^6}{15360 \pi G^2 M^2} \;</math>
+|}
+Where <math>P</math> is the energy outflow, ''<math>\hbar</math>'' is the [[reduced Planck constant]], <math>c</math> is the [[speed of light]], and <math>G</math> is the [[gravitational constant]]. It is worth mentioning that the above formula has not yet been derived in the framework of [[semiclassical gravity]].
+The power in the Hawking radiation from a [[solar mass]] (<math>M_{\odot}</math>) black hole turns out to be a minuscule 9 × 10<sup>−29</sup>&nbsp;watts. It is indeed an extremely good approximation to call such an object 'black'.
+:<math>P = \frac{\hbar c^6}{15360 \pi G^2 M_{\odot}^2} = 9.004 \times 10^{-29} \; \text{W} \;</math>
+Under the assumption of an otherwise empty universe, so that no [[matter]] or [[cosmic microwave background radiation]] falls into the black hole, it is possible to calculate how long it would take for the black hole to dissipate:
+:<math>K_{\operatorname{ev}} = \frac{\hbar c^6}{15360 \pi G^2} = 3.562 \times 10^{32} \; \text{W} \cdot \text{kg}^2 \;</math>
+Given that the power of the Hawking radiation is the rate of evaporation energy loss of the black hole:
+:<math>P = - \frac{dE}{dt} = \frac{K_{\operatorname{ev}}}{M^2} \;</math>
+Since the total energy E of the black hole is related to its mass M by Einstein's mass-energy formula:
+:<math>E = Mc^2 \;</math>
+:<math>P = - \frac{dE}{dt} = - \left( \frac{d}{dt} \right) M c^2 = -c^2 \frac{dM}{dt} \;</math>
+We can then equate this to our above expression for the power:
+:<math>-c^2 \frac{dM}{dt} = \frac{K_{\operatorname{ev}}}{M^2} \;</math>
+This differential equation is separable, and we can write:
+:<math>M^2 dM = - \frac{K_{\operatorname{ev}}}{c^2} dt \;</math>
+The black hole's mass is now a function ''M''(''t'') of time ''t''. Integrating over M from <math>M_0</math> (the initial mass of the black hole) to zero (complete evaporation), and over t from zero to <math>t_{\operatorname{ev}} \;</math>:
+:<math>\int_{M_0}^0 M^2 dM = - \frac{K_{\operatorname{ev}}}{c^2} \int_0^{t_{\operatorname{ev}}} dt \;</math>
+The evaporation time of a black hole is proportional to the cube of its mass:
+:<math>t_{\operatorname{ev}} = \frac{c^2 M_0^3}{3 K_{\operatorname{ev}}} = \left( \frac{c^2 M_0^3}{3} \right) \left( \frac{15360 \pi G^2}{\hbar c^6} \right) = \frac{5120 \pi G^2 M_0^3}{\hbar c^4} = 8.410 \times 10^{-17} \left[\frac{M_0}{\mathrm{kg}}\right]^3 \mathrm{s} \;</math>
+The time that the black hole takes to dissipate is:
+:{|cellpadding="2" style="border:2px solid #ccccff"
+|<math>t_{\operatorname{ev}} = \frac{5120 \pi G^2 M_0^{3}}{\hbar c^4} \;</math>
+|}
+Where <math>M_0</math> is the mass of the black hole.
+The lower classical quantum limit for mass for this equation is equivalent to the [[Planck mass]], <math>m_P</math>.
+Planck mass quantum black hole Hawking radiation evaporation time:
+:<math>t_{\operatorname{ev}} = \frac{5120 \pi G^2 m_P^3}{\hbar c^4} = 5120 \pi t_P = 5120 \pi \sqrt{\frac{\hbar G}{c^5}} = 8.671 \times 10^{-40} \; \text{s} \;</math>
+:{|cellpadding="2" style="border:2px solid #ccccff"
+|<math>t_{\operatorname{ev}} = 5120 \pi \sqrt{\frac{\hbar G}{c^5}} \;</math>
+|}
+Where <math>t_P</math> is the [[Planck time]].
+For a black hole of one [[solar mass]] (<math>M_{\odot}</math> = 1.98892 × 10<sup>30</sup>&nbsp;kg), we get an evaporation time of 2.098 × 10<sup>67</sup>&nbsp;years—much longer than the current [[big bang|age of the universe]] at 13.798 ± 0.037 x 10<sup>9 </sup>years.<ref name='planck_cosmological_parameters'>{{cite journal | arxiv=1303.5076 | title=Planck 2013 results. XVI. Cosmological parameters | author=Planck collaboration | journal=Submitted to Astronomy & Astrophysics | year=2013|bibcode = 2013arXiv1303.5076P }}</ref>
+:<math>t_{\operatorname{ev}} = \frac{5120 \pi G^2 M_{\odot}^3}{\hbar c^4} = 6.617 \times 10^{74} \; \text{s} \;</math>
+But for a black hole of 10<sup>11</sup>&nbsp;kg, the evaporation time is 2.667&nbsp;billion years. This is why some astronomers are searching for signs of exploding [[primordial black holes]].
+However, since the universe contains the [[cosmic microwave background radiation]], in order for the black hole to dissipate, it must have a temperature greater than that of the present-day black-body radiation of the universe of 2.7 K = 2.3 × 10<sup>−4</sup> eV. This implies that <math>M</math> must be less than 0.8 of the mass of the [[Earth]]<ref>[http://arxiv.org/abs/astro-ph/9911309 [astro-ph/9911309&#93; The Last Eight Minutes of a Primordial Black Hole<!-- Bot generated title -->]</ref> - approximately the mass of the [[Moon]].
+[[Cosmic microwave background radiation]] universe temperature:
+:<math>T_u = 2.725 \; \text{K} \;</math>
+Hawking total black hole mass:
+:<math>M_H \leq \frac{\hbar c^3}{8 \pi G k_B T_u} \leq 4.503 \times 10^{22} \; \text{kg} \;</math>
+:{|cellpadding="2" style="border:2px solid #ccccff"
+|<math>M_H \leq \frac{\hbar c^3}{8 \pi G k_B T_u} \;</math>
+|}
+:<math>\frac{M_H}{M_{\oplus}} = 7.539 \times 10^{-3} = 0.754 \; \% \;</math>
+Where, <math>M_{\oplus}</math> is the total [[Earth]] mass.
+In common units,
+:<math>P = 3.563 \, 45 \times 10^{32} \left[\frac{\mathrm{kg}}{M}\right]^2 \mathrm{W} \;</math>
+:<math>t_\mathrm{ev} = 8.407 \, 16 \times 10^{-17} \left[\frac{M_0}{\mathrm{kg}}\right]^3 \mathrm{s}
+\ \ \approx\ 2.66 \times 10^{-24} \left[\frac{M_0}{\mathrm{kg}}\right]^3 \mathrm{yr} \;</math>
+:<math>M_0 = 2.282 \, 71 \times 10^5 \left[\frac{t_\mathrm{ev}}{\mathrm{s}}\right]^{1/3} \mathrm{kg}
+\ \ \approx\ 7.2 \times 10^7 \left[\frac{t_\mathrm{ev}}{\mathrm{yr}}\right]^{1/3} \mathrm{kg} \;</math>
+So, for instance, a 1-second-lived black hole has a mass of 2.28 × 10<sup>5</sup> kg, equivalent to an energy of 2.05 × 10<sup>22</sup> J that could be released by 5 × 10<sup>6</sup> [[TNT equivalent|megatons of TNT]].
+The initial power is 6.84 × 10<sup>21</sup> W.
+Black hole evaporation has several significant consequences:
+* Black hole evaporation produces a more consistent view of [[black hole thermodynamics]], by showing how black holes interact thermally with the rest of the universe.
+* Unlike most objects, a black hole's temperature increases as it radiates away mass. The rate of temperature increase is exponential, with the most likely endpoint being the dissolution of the black hole in a violent burst of [[gamma ray]]s. A complete description of this dissolution requires a model of [[quantum gravity]], however, as it occurs when the black hole approaches [[Planck mass]] and [[planck length|Planck radius]].
+* The simplest models of black hole evaporation lead to the black hole information paradox. The information content of a black hole appears to be lost when it dissipates, as under these models the Hawking radiation is random (it has no relation to the original information). A number of solutions to this problem have been proposed, including suggestions that Hawking radiation is perturbed to contain the missing information, that the Hawking evaporation leaves some form of remnant particle containing the missing information, and that information is allowed to be lost under these conditions.
+==Large extra dimensions==
+Formulae from the previous section are only applicable if laws of gravity are approximately valid all the way down to the Planck scale. In particular, for black holes with masses below Planck mass (~10<sup>−5</sup> g), they result in unphysical lifetimes below Planck time (~10<sup>−43</sup> s). This is normally seen as an indication that Planck mass is the lower limit on the mass of a black hole.
+In the model with [[large extra dimension]]s, values of Planck constants can be radically different, and formulas for Hawking radiation have to be modified as well. In particular, the lifetime of a micro black hole (with radius below the scale of extra dimensions) is given by
+:<math>\tau \sim {1 \over M_*} \Bigl( {M_{BH} \over M_*} \Bigr) ^{(n+3)/(n+1)} </math>
+where <math>M_*</math> is the low energy scale (which could be as low as a few TeV), and ''n'' is the number of large extra dimensions. This formula is now consistent with black holes as light as a few TeV, with lifetimes on the order of "new Planck time" ~10<sup>−26</sup> s.
+==Experimental observation of Hawking radiation==
+Under experimentally achievable conditions for gravitational systems this effect is too small to be observed directly. In September 2010, however, an experimental set-up created a laboratory "white hole event horizon" that the experimenters claimed was shown to radiate Hawking radiation,<ref>[http://www.technologyreview.com/blog/arxiv/25805/ "First Observation of Hawking Radiation"] from the ''[[Technology Review]]''</ref> although its status as a genuine confirmation remains in doubt.<ref>{{cite journal|author=Matson, John|title=Artificial event horizon emits laboratory analog to theoretical black hole radiation|journal=Sci. Am|date=Oct 1, 2010|url=http://www.scientificamerican.com/article.cfm?id=hawking-radiation}}</ref> Some scientists predict that Hawking radiation could be studied by analogy using [[sonic black hole]]s, in which [[phonon|sound perturbations]] are analogous to light in a gravitational black hole and the flow of an approximately [[perfect fluid]] is analogous to gravity.<ref>C. Barceló, S. Liberati and M. Visser, “Towards the observation of Hawking radiation in Bose–Einstein condensates,” [http://arxiv.org/abs/gr-qc/0110036 arXiv:gr-qc/0110036] Int. J. Mod. Phys. A 18, 3735 (2003) .</ref>
+==See also==
+*[[Black hole starship]]
+*[[Thorne–Hawking–Preskill bet]]
+*[[Gibbons-Hawking effect]]
+==Notes==
+{{Reflist|30em}}
+==Further reading==
+*{{cite journal |last=Hawking |first=S. W. |authorlink= |coauthors= |year=1974 |month= |title=Black hole explosions? |journal=Nature |volume=248 |issue=5443 |page=30 |doi=10.1038/248030a0 |url= |accessdate= |bibcode = 1974Natur.248...30H }} → Hawking's first article on the topic
+*{{cite journal |last=Page |first=Don N. |authorlink= |coauthors= |year=1976 |month= |title=Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole |journal=Physical Review D |volume=13 |issue=2 |pages=198&ndash;206 |doi=10.1103/PhysRevD.13.198 |url= |accessdate= |bibcode = 1976PhRvD..13..198P }} → first detailed studies of the evaporation mechanism
+*{{cite journal |last=Carr |first=B. J. |authorlink= |coauthors=Hawking, S. W. |year=1974 |month= |title=Black holes in the early universe |journal=Monthly Notices of the Royal Astronomical Society |volume=168 |issue=2 |pages=399&ndash;415 |bibcode=1974MNRAS.168..399C |url= |accessdate= |quote= }} → links between primordial black holes and the early universe
+*{{cite journal |last=Barrau |first=A. |authorlink= |coauthors=''et al.'' |year=2002 |month= |title=Antiprotons from primordial black holes |journal=Astronomy &amp; Astrophysics |volume=388 |issue= 2|pages=676&ndash;687 |doi=10.1051/0004-6361:20020313 |url= |accessdate= |arxiv = astro-ph/0112486 |bibcode = 2002A&A...388..676B }}
+*{{cite journal |last=Barrau |first=A. |authorlink= |coauthors=''et al.'' |year=2003 |month= |title=Antideuterons as a probe of primordial black holes |journal=Astronomy &amp; Astrophysics |volume=398 |issue= 2|pages=403&ndash;410 |doi=10.1051/0004-6361:20021588 |url= |accessdate= |arxiv = astro-ph/0207395 |bibcode = 2003A&A...398..403B }}
+*{{cite journal |last=Barrau |first=A. |authorlink= |coauthors=Féron, C.; Grain, J. |year=2005 |month= |title=Astrophysical Production of Microscopic Black Holes in a Low–Planck-Scale World |journal=American Astronomical Society |volume=630 |issue= 2|pages=1015&ndash;1019 |doi=10.1086/432033 |url= |accessdate= |arxiv = astro-ph/0505436 |bibcode = 2005ApJ...630.1015B }} → experimental searches for primordial black holes thanks to the emitted antimatter
+*{{cite arXiv |last=Barrau |first=A. |author= |authorlink= |coauthors=Boudoul, G. |title=Some aspects of primordial black hole physics |version= |pages= |date= |url= |eprint=astro-ph/0212225 |accessdate= }} → cosmology with primordial black holes
+*{{cite journal |last=Barrau |first=A. |authorlink= |coauthors=Grain, J.; Alexeyev, S. O. |year=2004 |month= |title=Gauss–Bonnet black holes at the LHC: beyond the dimensionality of space |journal=Physics Letters B |volume=584 |issue=1&ndash;2 |pages=114&ndash;122 |doi=10.1016/j.physletb.2004.01.019 |url= |accessdate= |arxiv = hep-ph/0311238 |bibcode = 2004PhLB..584..114B }} → searches for new physics (quantum gravity) with primordial black holes
+*{{cite journal |last=Kanti |first=Panagiota |authorlink= |coauthors= |year=2004 |month= |title=Black Holes in Theories with Large Extra Dimensions: a Review |journal=International Journal of Modern Physics A |volume=19 |issue=29 |pages=4899&ndash;4951 |doi=10.1142/S0217751X04018324 |url= |accessdate= |arxiv = hep-ph/0402168 |bibcode = 2004IJMPA..19.4899K }} → evaporating black holes and extra-dimensions
+*D. Ida, K.-y. Oda & S.C.Park, [http://arxiv.org/abs/hep-th/0212108, Phys. Rev. D67 (2003) 064025],[http://arxiv.org/abs/hep-th/0503052, Phys. Rev. D71 (2005) 124039],[http://arxiv.org/abs/hep-th/0602188]: determination of black hole's life and extra-dimensions
+*N. Nicolaevici, J. Phys. A: Math. Gen. 36 (2003) 7667-7677 [http://www.iop.org/EJ/abstract/0305-4470/36/27/317/]: consistent derivation of the Hawking radiation in the Fulling-Davies mirror model.
+*L. Smolin, [http://www.physicstoday.org/vol-59/iss-11/pdf/vol59no11p44_48.pdf Quantum gravity faces reality], consists of the recent developments and predictions of [[loop quantum gravity]] about gravity in small scales including the deviation from Hawking radiation effect by Ansari [http://arxiv.org/hep-th/0607081 Spectroscopy of a canonically quantized horizon].
+*M. Ansari, [http://xxx.lanl.gov/abs/hep-th/0607081 Area, ladder symmetry, degeneracy and fluctuations of a horizon] studies the deviation of a loop quantized black hole from Hawking radiation. A novel observable quantum effect of black hole quantization is introduced.
+*Stuart L. Shapiro, Saul A. Teukolsky (1983), Black holes, white dwarfs, and neutron stars: The physics of compact objects. p.&nbsp;366 Wiley-Interscience, Hawking radiation evaporation formula derivation.
+*{{Cite journal| last = Leonhardt | first = Ulf | authorlink = | coauthors= Maia, Clovis; Schuetzhold, Ralf|  year = 2010 | month = | title = Focus on Classical and Quantum Analogs for Gravitational Phenomena and Related Effects | journal = [[New Journal of Physics]] | volume =  | issue =  | pages = | doi =  | url = http://iopscience.iop.org/1367-2630/focus/Focus%20on%20Classical%20and%20Quantum%20Analogues%20for%20Gravitational%20Phenomena%20and%20Related%20Effects | accessdate = | quote =}}
+==External links==
+*[http://xaonon.dyndns.org/hawking/ Hawking radiation calculator tool]
+*[http://www.cerncourier.com/main/article/44/9/22 The case for mini black holes] A. Barrau & J. Grain explain how the Hawking radiation could be detected at colliders
+*[http://casa.colorado.edu/~ajsh/hawk.html University of Colorado at Boulder]
+*[http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=448732 Hawking radiation on arxiv.org]
+*[http://news.slashdot.org/story/10/09/27/1256236/Hawking-Radiation-Claimed-Created-In-a-Lab Hawking radiation observed in laboratory?]
+{{quantum gravity}}
+{{Stephen Hawking}}
+{{DEFAULTSORT:Hawking Radiation}}
+[[Category:Black holes]]
+[[Category:Quantum field theory]]
+[[Category:Stephen Hawking]]
+[[Category:Astronomical hypotheses]]

9 (number): Difference between revisions

Revision as of 15:46, 31 January 2014

Overview

Trans-Planckian problem

Emission process

Black hole evaporation

Large extra dimensions

Experimental observation of Hawking radiation

See also

Notes

Further reading

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