black hole spacetimes | vanishing angular momentum | positive angular momentum |
---|---|---|
vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
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The theory of gravity in $3+1$ dimensions famously has black hole solutions, being the limiting configuration of a point mass gravitational source. In higher dimensional gravity, and in particular in higher dimensional supergravity, there are analogous solutions, which however are limiting configurations of a gravitational source that is supported on a line, or a surface, or a higher dimensional space. For a surface one might speak of black membrane solutions hence generally of black brane solutions.
Particularly the BPS states among the black branes in supergravity, i.e. those solutions that carry Killing spinors, include configurations that look like the strong-coupling version of the Green-Schwarz super p-branes.
1/2 BPS black branes in supergravity: D-branes, F1-brane, NS5-brane, M2-brane, M5-brane
(table taken from Blumenhagen-Lüst-Theisen “Basic concepts of string theory”)
The near-horizon geometry of these black branes is generically that of anti de Sitter spacetime times a sphere. To the extent that the worldvolume theory of the branes is a superconformal QFT, this is the origin of the AdS-CFT correspondence.
The types of black branes that can occur in theories of supergravity that are obtained from the maximal 11-dimensional supergravity match precisely the types of D-branes and NS-branes that appear in the corresponding perturbative superstring theories.
The idea is that both these brane-phenomena are aspects of one single entity:
At low string coupling the D-brane/NS-brane description is accurate. Low string coupling implies that the coupling of gravity is weak, hence that the back-reaction of the branes on the background geometry is negligible.
At large string coupling but low energy, the effective supergravity description becomes accurate. Here the branes do back-react on the gravitational background and hence create the black brane spacetime geometry.
This duality of the brane picture is at the heart of the AdS/CFT correspondence. See there for more details.
black membrane?
Table of branes appearing in supergravity/string theory (for classification see at brane scan).
See also
Original articles include
Michael Duff, J. X. Lu, Black and super $p$-branes in diverse dimensions (arXiv:hep-th/9306052)
Michael Duff, H. Lu, Christopher Pope, The Black Branes of M-theory, Phys.Lett.B382:73-80,1996 (arXiv:hep-th/9604052)
The M5-brane was maybe first found as a black brane of 11-dimensional supergravity (the black fivebrane) in
The observation that black $p$-branes metric for odd $p$ are completely non-singular is due to
The suggestion that extremal/BPS state black branes are the strong coupling incarnation of fundamental branes originates in
Chris Hull, Paul Townsend, Unity of Superstring Dualities, Nucl.Phys.B438:109-137,1995 (arXiv:hep-th/9410167)
Edward Witten, bottom of p. 6 of String Theory Dynamics In Various Dimensions, Nucl.Phys.B443:85-126,1995 (arXiv:hep-th/9503124)
Review includes,
Mike Duff, chapter 5 of The World in Eleven Dimensions: Supergravity, Supermembranes and M-theory, IoP 1999 (publisher)
Kellogg Stelle, around section 3.3. of BPS Branes in Supergravity (arXiv:hep-th/9803116)
Ofer Aharony, S.S. Gubser, Juan Maldacena, H. Ooguri, Y. Oz, section 1.3 of Large N Field Theories, String Theory and Gravity (arXiv:hep-th/9905111)
Thomas Mohaupt, Black holes in supergravity and string theory, Class. Quantum Grav. 17 (2000) 3429–3482 (pdf)
Ralph Blumenhagen, Dieter Lüst, Stefan Theisen, Brane solutions in supergravity, chapter 18.5 in Basic Concepts of String Theory Part of the series Theoretical and Mathematical Physics pp 585-639 Springer 2013
and in the context of multiple M2-branes in the BLG model:
Further developments include
Gerard Clement, Dmitri Gal’tsov, Cedric Leygnac, Black branes on the linear dilaton background, Phys. Rev. D71 (2005) 084014 (arXiv:hep-th/0412321)
D. Gal’tsov, S. Klevtsov, D. Orlov, G. Clement, More on general $p$-brane solutions, Int.J.Mod.Phys.A21:3575-3604, 2006 (arXiv:hep-th/0508070)
Michael Duff, Near-horizon brane scan revived, Nucl. Phys. B810:193-209, 2009 (arXiv:0804.3675)
Jay Armas, Joan Camps, Troels Harmark, Niels A. Obers, The Young Modulus of Black Strings and the Fine Structure of Blackfolds (arXiv:1110.4835)