Generalized Verma module - Revision history

en>Colonies Chris: sp, date & link fixes; unlinking common words, replaced: Poincaré-Birkhoff-Witt → Poincaré–Birkhoff–Witt using AWB

2014-03-11T22:58:41Z

sp, date & link fixes; unlinking common words, replaced: Poincaré-Birkhoff-Witt → Poincaré–Birkhoff–Witt using AWB

← Older revision		Revision as of 00:58, 12 March 2014
Line 1:		Line 1:
	~~{{tone\|date=April 2013}}~~
	The '''BTZ black hole''', named after [[Máximo Bañados]], [[Claudio Teitelboim]], and [[Jorge Zanelli]], is a [[black hole]] solution for [[(2+1)-dimensional topological gravity\|(2+1)-dimensional]] gravity with a negative [[cosmological constant]].

	~~== History ==~~
	In 1992 Bañados, Teitelboim and Zanelli discovered BTZ black hole{{harv\|Bañados\|Teitelboim\|Zanelli\|1992}}. At that time, it came as a surprise because it is believed that no black hole solutions are shown to exist for a negative cosmological constant and BTZ black hole has remarkably similar properties to the 3+1 dimensional black hole, which would exist in our real universe.

	~~When the cosmological constant is zero, a vacuum solution of (2+1)-dimensional gravity is necessarily flat~~, ~~and~~ it ~~can be shown that no black hole solutions exist{{Citation needed\|date=October 2011}}~~. ~~By introducing [[dilaton]]s, we~~ can have black holes.{{verify source\|date=April 2013}} We do have conical angle deficit solutions, but they don't have event horizons. It therefore came as a surprise when black hole solutions were shown to exist for a negative cosmological constant.		If you present photography effectively, it helps you look much more properly at the globe around you. This means you can setup your mailing list and auto-responder on your wordpress site and then you can add your subscription form to any other blog, splash page, capture page or any other site you like. SEO Ultimate - I think this plugin deserves more recognition than it's gotten up till now. In the recent years, there has been a notable rise in the number of companies hiring Indian Word - Press developers. You can customize the appearance with PSD to Word - Press conversion ''. <br><br>purcase and download - WPZOOM Tribune wordpress Theme, find and use the WPZOOM Discount Code. Best of all, you can still have all the functionality that you desire when you use the Word - Press platform. This plugin allows a blogger get more Facebook fans on the related fan page. Apart from these, you are also required to give some backlinks on other sites as well. By using Word - Press, you can develop very rich, user-friendly and full-functional website. <br><br>If you liked this posting and you would like to acquire a lot more facts pertaining to [http://www.noo.ru/cgi-bin/addrelnx.cgi?file=Main/RealitySynthesis/Lithium/golubitsa wordpress dropbox backup] kindly stop by our own internet site. The entrepreneurs can easily captivate their readers by using these versatile themes. Browse through the popular Wordpress theme clubs like the Elegant Themes, Studio Press, Woo - Themes, Rocket Theme, Simple Themes and many more. This platform can be customizedaccording to the requirements of the business. Newer programs allow website owners and internet marketers to automatically and dynamically change words in their content to match the keywords entered by their web visitors in their search queries'a feat that they cannot easily achieve with older software. Premium vs Customised Word - Press Themes - Premium themes are a lot like customised themes but without the customised price and without the wait. <br><br>Word - Press has plenty of SEO benefits over Joomla and Drupal. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. Exacting subjects in reality must be accumulated in head ahead of planning on your high quality theme. The company gains commission from the customers' payment. See a product, take a picture, and it gives you an Amazon price for that product, or related products. <br><br>There is no denying that Magento is an ideal platform for building ecommerce websites, as it comes with an astounding number of options that can help your online business do extremely well. Automated deal feed integration option to populate your blog with relevant deals. However, you must also manually approve or reject comments so that your website does not promote parasitic behavior. Thus, Word - Press is a good alternative if you are looking for free blogging software. Get started today so that people searching for your type of business will be directed to you.

	~~== Properties ==~~
	~~The similarities to the ordinary black holes in 3+1　dimensions:~~
	*It has "no hairs" ([[No hair theorem]]) and ~~is fully characterized by [[ADM formalism\|ADM~~-~~mass]]~~, ~~angular momentum and charge.~~
	*It has the same [[Black hole thermodynamics\|thermodynamical properties]] as the ordinary black holes, ~~e.g~~. ~~its entropy is captured by a law directly analogous to the [[Bekenstein bound]] in (3+1)~~-~~dimensions, essentially with the surface area replaced by the BTZ black hole~~'s ~~circumference~~.
	*Like the ~~[[Kerr black hole]]~~, a ~~rotating BTZ black hole contains an inner and an outer horizon. see also [[Ergosphere]].~~

	~~Since (2+1)-dimensional gravity has no [[Newtonian limit]], one might fear that~~ the ~~BTZ black hole is not the final state~~ of ~~a [[gravitational collapse]]~~. ~~It was however shown, that this black hole could arise from collapsing matter and we~~ can ~~calculate~~ the ~~energy~~-~~moment tensor of BTZ as same as (3+1) black holes. {{harv\|Carlip\|1995}} section 3 Black Holes and Gravitational Collapse~~.
	<~~!--not in any spacetime known to exist--~~>

	~~The BTZ solution is often discussed in the realm on (2+1)-dimensional [[quantum gravity]].~~

	~~== The case without charge ==~~
	~~The metric in the absence of charge is~~
	:<~~math~~>~~ds^2 = -\frac{(r^2 - r_+^2)(r^2 - r_-^2)}{l^2 r^2}dt^2 + \frac{l^2 r^2 dr^2}{(r^2 - r_+^2)(r^2~~ - ~~r_-^2)} + r^2 \left(d\phi - \frac{r_+ r_-}{l r^2} dt \right)^2 </math>~~
	~~where <math>r_+~~,~~~r_- </math> are the black hole radii~~ and ~~<math>l </math> is~~ the ~~radius of AdS<sub>3</sub> space~~. ~~The mass and angular momentum~~ of the ~~black hole is~~
	~~: <math> M = \frac{r_+^2 + r_~~-~~^2}{l^2}~~,~~~~~~~J = \frac{2r_+ r_-}{l} </math>~~

	~~BTZ black holes without any electric charge~~ are ~~locally isometric~~ to ~~[[anti de Sitter space]]~~. ~~More precisely~~, ~~it corresponds to an [[orbifold]] of the [[universal covering space]] of AdS~~<~~sub~~>3<~~/sub~~>.

	~~A rotating BTZ black hole admits~~ [~~[closed timelike curve]]s.~~

	~~==See also==~~
	*[[Axial symmetry\|axi-symmetric spacetime]]

	~~== References ==~~
	~~;Notes~~
	~~<references~~/>

	~~;Bibliography~~
	*{{Citation \| last1=Bañados \| first1=Máximo \| last2=Teitelboim \| first2=Claudio \| last3=Zanelli \| first3=Jorge \| title=The Black hole in three-dimensional space-time \|series=Phys.~~Rev~~.~~Lett. \|volume=69 \| publisher=[[American Physical Society]] \| year=1992 \| pages= 1849–1851　}}url=http:~~//~~arxiv~~.~~org~~/~~pdf~~/~~hep-th~~/~~9204099v3~~.~~pdf~~
	*{{Citation \| last=Carlip \| first=Steven \| title=Conformal Field Theory, ~~(2+1)~~-~~Dimensional Gravity~~, and the ~~BTZ Black Hole \|series=arxiv \| year=2005 }}url=http://arxiv~~.~~org/pdf/gr~~-~~qc/0503022v4.pdf~~
	*{{Citation \| last=Carlip \| first=Steven \| title=The (2+1)-~~Dimensional Black Hole \|series=arxiv \| year=1995 }}url=http://arxiv~~.~~org/pdf/gr~~-~~qc/9506079~~.~~pdf~~
	*{{Citation \| last=Bañados \| first=Máximo \| title=Three-~~dimensional quantum geometry and black holes \|series=arxiv \| year=1999 }}url=http://arxiv.org/abs/hep~~-~~th/9901148v3~~.~~pdf~~
	*{{Citation \| last=Daisuke \| first=Ida \| title=No Black Hole Theorem in ~~Three-Dimensional Gravity \|series=Phys~~. ~~Rev~~. ~~Lett~~. ~~85 3758 \| year=2000 }} url=http://arxiv~~.~~org/abs/gr~~-~~qc/0005129~~

	~~{{Time travel}}~~

	~~{{DEFAULTSORT:Btz Black Hole}}~~
	~~[[Category:Black holes]]~~
	~~[[Category:Quantum gravity]]~~
	~~[[Category:Mathematical methods in general relativity]]~~

en>Yobot: WP:CHECKWIKI errors fixed + general fixes using AWB (8961)

2013-03-07T20:44:33Z

WP:CHECKWIKI errors fixed + general fixes using AWB (8961)

← Older revision		Revision as of 22:44, 7 March 2013
Line 1:		Line 1:
	It'~~s April 14~~ and ~~the Sony PSN or PlayStation Community down standing mills about. And whereas the service struggles to stand up and back on-line~~, a ~~non~~-~~public letter to PS3 publishers leaked into the general public area~~.~~<br><br>This nude celeb hacking scandal started in 2010~~, and ~~the most recent experiences say~~ that the ~~FBI is closing~~ in on the ~~hackers accountable. The problem~~ is, ~~any person else will probably take over if one is caught. These nude leaked photos~~ of ~~celebs are obviously large money makers. It~~ is ~~unhappy~~ that ~~Scarlett Johansson has been targeted by hackers so many~~ [~~http://www~~.~~Bing~~.~~com/search?q~~=~~occasions&form~~=~~MSNNWS&mkt~~=~~en-us&pq~~=~~occasions occasions~~]~~. Clearly it~~ is ~~a part of being well~~-~~known~~, ~~however it isn't one of many good parts~~.~~<br><br>Download Dungeon For Android Add unlimited Gems Unlimited Energy & Health We have been into~~ the ~~game for just~~ a ~~few hours and taking part~~ in ~~the three characters. Beneath are our first impressions on Eternity Warriors~~ 3, the ~~third installment of Eternity Warriors sequence. Moreover two new characters, I~~'~~ve already seen an enormous world rendered in tremendous detailed 3D~~. ~~Compared to~~ the ~~earlier two games~~, ~~Eternity Warriors 3 world looks more stunning~~ and ~~massive~~. ~~After~~ 2 ~~hours into just~~ a ~~few dungeons~~ , ~~I run into issues~~ of ~~defeating monsters~~ and ~~bosses~~. ~~Rapidly, I discovered some gamers said within the Chat we will crew up with other gamers~~ to co-~~overcome~~ the ~~difficulties~~. ~~But I did not use this function. EXPERIENCE A TRUE RPG Finest Cydia Video games Gameboy Gallery 3 Grand Theft Auto three LOOT a large number~~ of ~~objects~~<br><br>~~On April 21~~, the ~~corporate announced that~~ the ~~PSN could be back up in a day or two after~~ the ~~investigation was full. On April 22~~, ~~Sony announced its PS3 PlayStation Community had been hacked, but it didn't provide~~ any ~~extra info. Individuals grew~~ to ~~become involved at this point~~. ~~On April 23~~, ~~the company announced~~ it ~~needed~~ to ~~rebuild its~~ [~~http://Community.org community~~] ~~after~~ the ~~hack. Individuals started to get involved that this hack was important if the community needed to be rebuilt.~~<br><br>~~We now have launched the most recent Dungeon Hunter four Android aps Hack~~. Obtain Dungeon Hunter four Hack without delay and turn out to be the best player! Downloaded file accommodates Dungeon Hunter 4 Hack that provides you possibility to gain extra gems, gold and harms as well as different helpful choices- ~~reminiscent of powerful gears, boosts and abilities~~. ~~You could be sure it's 100% working and virus free because our~~ [http://~~natasasrnka2213~~.~~tumblr~~.~~com~~/~~post~~/~~100065346496~~/~~dungeon~~-~~hunter~~-4-~~hack~~-~~tool~~-~~cheats Dungeon Hunter 4 Hack] was scanned several occasions with ESET Anti~~- ~~Virus earlier than uploading here~~. ~~It is usually free to download~~. ~~You may obtain Dungeon Hunter four Hack below~~.		{{tone\|date=April 2013}}
			The '''BTZ black hole''', named after [[Máximo Bañados]], [[Claudio Teitelboim]], and [[Jorge Zanelli]], is a [[black hole]] solution for [[(2+1)-dimensional topological gravity\|(2+1)-dimensional]] gravity with a negative [[cosmological constant]].

			== History ==
			In 1992 Bañados, Teitelboim and Zanelli discovered BTZ black hole{{harv\|Bañados\|Teitelboim\|Zanelli\|1992}}. At that time, it came as a surprise because it is believed that no black hole solutions are shown to exist for a negative cosmological constant and BTZ black hole has remarkably similar properties to the 3+1 dimensional black hole, which would exist in our real universe.

			When the cosmological constant is zero, a vacuum solution of (2+1)-dimensional gravity is necessarily flat, and it can be shown that no black hole solutions exist{{Citation needed\|date=October 2011}}. By introducing [[dilaton]]s, we can have black holes.{{verify source\|date=April 2013}} We do have conical angle deficit solutions, but they don't have event horizons. It therefore came as a surprise when black hole solutions were shown to exist for a negative cosmological constant.

			== Properties ==
			The similarities to the ordinary black holes in 3+1　dimensions:
			*It has "no hairs" ([[No hair theorem]]) and is fully characterized by [[ADM formalism\|ADM-mass]], angular momentum and charge.
			*It has the same [[Black hole thermodynamics\|thermodynamical properties]] as the ordinary black holes, e.g. its entropy is captured by a law directly analogous to the [[Bekenstein bound]] in (3+1)-dimensions, essentially with the surface area replaced by the BTZ black hole's circumference.
			*Like the [[Kerr black hole]], a rotating BTZ black hole contains an inner and an outer horizon. see also [[Ergosphere]].

			Since (2+1)-dimensional gravity has no [[Newtonian limit]], one might fear that the BTZ black hole is not the final state of a [[gravitational collapse]]. It was however shown, that this black hole could arise from collapsing matter and we can calculate the energy-moment tensor of BTZ as same as (3+1) black holes. {{harv\|Carlip\|1995}} section 3 Black Holes and Gravitational Collapse.
			<!--not in any spacetime known to exist-->

			The BTZ solution is often discussed in the realm on (2+1)-dimensional [[quantum gravity]].

			== The case without charge ==
			The metric in the absence of charge is
			:<math>ds^2 = -\frac{(r^2 - r_+^2)(r^2 - r_-^2)}{l^2 r^2}dt^2 + \frac{l^2 r^2 dr^2}{(r^2 - r_+^2)(r^2 - r_-^2)} + r^2 \left(d\phi - \frac{r_+ r_-}{l r^2} dt \right)^2 </math>
			where <math>r_+,~r_- </math> are the black hole radii and <math>l </math> is the radius of AdS<sub>3</sub> space. The mass and angular momentum of the black hole is
			: <math> M = \frac{r_+^2 + r_-^2}{l^2},~~~~~J = \frac{2r_+ r_-}{l} </math>

			BTZ black holes without any electric charge are locally isometric to [[anti de Sitter space]]. More precisely, it corresponds to an [[orbifold]] of the [[universal covering space]] of AdS<sub>3</sub>.

			A rotating BTZ black hole admits [[closed timelike curve]]s.

			==See also==
			*[[Axial symmetry\|axi-symmetric spacetime]]

			== References ==
			;Notes
			<references/>

			;Bibliography
			*{{Citation \| last1=Bañados \| first1=Máximo \| last2=Teitelboim \| first2=Claudio \| last3=Zanelli \| first3=Jorge \| title=The Black hole in three-dimensional space-time \|series=Phys.Rev.Lett. \|volume=69 \| publisher=[[American Physical Society]] \| year=1992 \| pages= 1849–1851　}}url=http://arxiv.org/pdf/hep-th/9204099v3.pdf
			*{{Citation \| last=Carlip \| first=Steven \| title=Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole \|series=arxiv \| year=2005 }}url=http://arxiv.org/pdf/gr-qc/0503022v4.pdf
			*{{Citation \| last=Carlip \| first=Steven \| title=The (2+1)-Dimensional Black Hole \|series=arxiv \| year=1995 }}url=http://arxiv.org/pdf/gr-qc/9506079.pdf
			*{{Citation \| last=Bañados \| first=Máximo \| title=Three-dimensional quantum geometry and black holes \|series=arxiv \| year=1999 }}url=http://arxiv.org/abs/hep-th/9901148v3.pdf
			*{{Citation \| last=Daisuke \| first=Ida \| title=No Black Hole Theorem in Three-Dimensional Gravity \|series=Phys. Rev. Lett. 85 3758 \| year=2000 }} url=http://arxiv.org/abs/gr-qc/0005129

			{{Time travel}}

			{{DEFAULTSORT:Btz Black Hole}}
			[[Category:Black holes]]
			[[Category:Quantum gravity]]
			[[Category:Mathematical methods in general relativity]]

en>Vyom25: Disambiguated: Harish-Chandra theorem → Harish-Chandra's regularity theorem

2012-04-08T11:54:45Z

Disambiguated: Harish-Chandra theorem → Harish-Chandra's regularity theorem

New page

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