black hole spacetimes | vanishing angular momentum | positive angular momentum |
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positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
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In gravity, Bekenstein-Hawking entropy is an entropy assigned to black hole, on the basis of laws of thermodynamics and observers outside black hole. It striking property is that it is proportional to the surface area of the balck hole’s horizon.
In the context of string theory BH entropy is explained by a version of the AdS/CFT correspondence. Here every black brane solution in supergravity is the strong-coupling limit of a D-brane worldvolume QFT. After KK-reduction these black brane configurations become ordinary black holes. The entropy of the D-brane worldvolume theories on the event horizon turns out to coincide with the BH entropy of the corresponding black hole.
Detailed computations exist in particular for D1-brane/D5-brane systems. This is parts of the AdS/CFT correspondence. See (AGMOO, chapter 5).
See also
Another way to derive Bekenstein-Hawking entropy in string theory is by computing the entropy of weakly coupled open strings on D-brane configurations in flat Minkowski space which transmute as the coupling constant is increased to given (supersymmetric) black hole configurations. More on this is at black holes in string theory.
gravitational entropy
Bekenstein-Hawking entropy
Basic introductory accounts include
Robert Wald, The Thermodynamics of Black Holes (arXiv:gr-qc/9912119)
Jacob Bekenstein, Bekenstein-Hawking entropy, (2008), Scholarpedia, 3(10):7375
A more general discussion which identifies thermodynamic properties of all horizons appearing on gravity (not just black hole horizons) was given in
This article showed that under some assumptions the Einstein equations can even be derived from identifying gravitational horizon area with entropy and them imposing laws of thermodynamics.
For more comments and more references on this observation see
(Later authors tried to argue that derivations like this show that gravity is not a fundamental force of nature such as electromagnetism or the strong nuclear force, but rather an entropic force that arises only from more fundamental forces in a thermodynamic limit. This however remains at best unclear.)
Discussion of black hole entropy from entropy of conformal field theory associated with the horizon has been given in
Steve Carlip, Entropy from Conformal Field Theory at Killing Horizons, Class.Quant.Grav.16:3327-3348,1999 (arXiv:gr-qc/9906126)
Steve Carlip, Horizon Constraints and Black Hole Entropy, Class.Quant.Grav.22:1303-1312, 2005 (arXiv:hep-th/0408123)
and reviewed in
Steve Carlip, Horizon constraints and black hole entropy (arXiv:gr-qc/0508071)
Steve Carlip, Symmetries, Horizons, and Black Hole Entropy, Gen.Rel.Grav.39:1519-1523,2007; Int.J.Mod.Phys.D17:659-664,2008 (arXiv:0705.3024)
Further developments on black hole entropy are in
Ashoke Sen, Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions, JHEP04(2013)156 (arXiv:arXiv:1205.0971)
Aitor Lewkowycz, Juan Maldacena, Generalized gravitational entropy (arXiv:1304.4926)
A related controversial article that spawned a lot of discussion is
A survey of interpretation of black holes in string theory is in Chapter 5 of
Discussion in view of higher curvature corrections includes
See also
Discussions of the interpreation of BH entropy as entanglement entropy include