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| In [[mathematical physics]], a [[metric (mathematics)|metric]] describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region – essentially describing the intrinsic geometry of the region. An '''acoustic metric''' will describe the signal-carrying properties characteristic of a given particulate medium in [[acoustics]], or in [[fluid dynamics]]. Other descriptive names such as '''sonic metric''' are also sometimes used, interchangeably.
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| == A simple fluid example ==
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| For simplicity, we will assume that the underlying background geometry is [[Euclidean geometry|Euclidean]], and that this space is filled with an [[isotropic]] [[inviscid fluid]] at zero temperature (e.g. a [[superfluid]]). This fluid is described by a [[density field]] ρ and a [[velocity field]] <math>\vec{v}</math>. The speed of sound at any given point depends upon the [[compressibility]] which in turn depends upon the density at that point. This can be specified by the "speed of sound field" c. Now, the combination of both isotropy and [[Galilean covariance]] tells us that the permissible velocities of the sound waves at a given point x, <math>\vec{u}</math> has to satisfy
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| :<math>(\vec{u}-\vec{v}(x))^2=c(x)^2</math>
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| This restriction can also arise if we imagine that sound is like "light" moving though a spacetime described by an effective [[metric tensor]] called the '''acoustic metric'''.
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| The acoustic metric
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| <math>\mathbf{g}=g_{00}dt \otimes dt+2g_{0i}dx^i \otimes dt+g_{ij} dx^i \otimes dx^j</math>
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| "Light" moving with a velocity of <math>\vec{u}</math> (NOT the 4-velocity) has to satisfy
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| :<math>g_{00}+2g_{0i}u^i+g_{ij}u^i u^j=0</math>
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| If
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| :<math>g=\alpha^2\begin{pmatrix}-(c^2-v^2)&-\vec{v}\\-\vec{v}&\mathbf{1}\end{pmatrix}</math>
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| where α is some conformal factor which is yet to be determined (see [[Weyl rescaling]]), we get the desired velocity restriction. α may be some function of the density, for example.
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| ==Acoustic horizons==
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| {{Main|Sonic black holes}}
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| An acoustic metric can give rise to "acoustic horizons" (also known as "sonic horizons"), analogous to the event horizons in the spacetime metric of general relativity. However, unlike the spacetime metric, in which the invariant speed is the absolute upper limit on the propagation of all causal effects, the invariant speed in an acoustic metric is not the upper limit on propagation speeds. For example, the speed of sound is less than the speed of light. As a result, the horizons in acoustic metrics are not perfectly analogous to those associated with the spacetime metric. It is possible for certain physical effects to propagate back across an acoustic horizon. Such propagation is sometimes considered to be analogous to Hawking radiation, although the latter arises from quantum field effects in curved spacetime.
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| ==Acoustic metrics and quantum gravity==
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| Since acoustic metrics share some statistical behaviours with the way that we expect a future theory of quantum gravity to behave (such as [[Hawking radiation]]), these metrics have sometimes been studied in the hope that they might shed light on the [[statistical mechanics]] of actual black holes. Some people have suggested {{Citation needed|date=April 2010}} that analog models are more than just an analogy and that the actual gravity that we observe is actually an analog theory. But in order for this to hold, since a generic analog model depends upon BOTH the acoustic metric AND the underlying background geometry, the low energy large wavelength limit of the theory has to [[decouple]] from the background geometry.
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| ==See also==
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| * [[Analog models of gravity]]
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| * [[Hawking radiation]]
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| * [[gravastar]]
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| * [[acoustics]]
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| * [[metric (mathematics)]]
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| * [[quantum mechanics]]
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| * [[quantum gravity]]
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| ==References==
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| * <span style="color:darkblue;">W.G. Unruh, "Experimental black hole evaporation" Phys. Rev. Lett. '''46''' (1981), 1351–1353. </span>
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| : ''– considers information leakage through a transsonic horizon as an "analogue" of Hawking radiation in black hole problems''
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| * <span style="color:darkblue;">Matt Visser "Acoustic black holes: Horizons, ergospheres, and Hawking radiation" Class. Quant. Grav. '''15''' (1998), 1767–1791. [http://xxx.lanl.gov/abs/gr-qc/9712010 gr-qc/9712010]</span>
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| : ''– indirect radiation effects in the physics of acoustic horizon explored as a case of Hawking radiation ''
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| * <span style="color:darkblue;">Carlos Barceló, Stefano Liberati, and Matt Visser, "Analogue Gravity" [http://xxx.lanl.gov/abs/gr-qc/0505065 gr-qc/0505065]</span>
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| : ''– huge review article of "toy models" of gravitation, 2005, currently on v2, 152 pages, 435 references, alphabetical by author. ''
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| ==External links==
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| *[http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=-27385 Acoustic black holes on arxiv.org]
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| [[Category:Acoustics]]
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| [[Category:Quantum gravity]]
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Oscar is what my wife enjoys to call me and I completely dig that title. Since she was 18 she's been working as a meter reader but she's always needed her personal company. Puerto Rico is where he's been living for many years and he will by no means transfer. To perform baseball is the hobby he will never stop performing.
my weblog: http://www.animecontent.com