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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
Textbook account:
Review:
Review form the point of view of thermal field theory:
Basic introductory accounts:
Robert Wald, The Thermodynamics of Black Holes (arXiv:gr-qc/9912119)
Jacob Bekenstein, Bekenstein-Hawking entropy, (2008), Scholarpedia, 3(10):7375
and further review:
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 discussion of the “black hole firewall problem”:
Discussion via Wick rotation to Euclidean field theory on spacetimes with compact/periodic Euclidean time (thermal field theory on curved spacetimes) is in
S.A. Fulling, S.N.M. Ruijsenaars, Temperature, periodicity and horizons, Physics Reports Volume 152, Issue 3, August 1987, Pages 135-176 (pdf, doi:10.1016/0370-1573(87)90136-0)
Gary Gibbons, Malcolm J. Perry, Black Holes and Thermal Green Functions, Vol. 358, No. 1695 (1978) (jstor:79482)
Microscopic explanation of Bekenstein-Hawking entropy via geometric engineering of black holes in string theory as bound states of D-branes:
Review of interpretation of black holes in string theory includes
Ofer Aharony, S. S. Gubser, Juan Maldacena, Hirosi Ooguri, Y. Oz, Chapter 5 of Large N field theories, string theory and gravity, arXiv:hep-th/9905111
Per Kraus, Lectures on black holes and the $AdS_3/CFT_2$ correspondence, Lect. Notes Phys.755:193-247, 2008 (arXiv:hep-th/0609074)
Ashoke Sen, Black Hole Entropy Function, Attractors and Precision Counting of Microstates, Gen. Rel. Grav. 40: 2249-2431, 2008 (arXiv:0708.1270)
Dieter Lüst, Ward Vleeshouwers, sections 21-22 of Black Hole Information and Thermodynamics (arXiv:1809.01403)
Sebastian De Haro, Jeroen van Dongen, Manus Visser, Jeremy Butterfield, Conceptual Analysis of Black Hole Entropy in String Theory (arXiv:1904.03232)
Jeroen van Dongen, Sebastian De Haro, Manus Visser, Jeremy Butterfield, Emergence and Correspondence for String Theory Black Holes (arXiv:1904.03234)
Discussion in view of higher curvature corrections includes
See also
Discussions of the interpreation of BH entropy as holographic entanglement entropy include
Computation of black hole entropy in 4d via AdS4-CFT3 duality from holographic entanglement entropy in the ABJM theory for the M2-brane is discussed in
Claim that the proper application of holographic entanglement entropy to the discussion of Bekenstein-Hawking entropy resolves the apparent black hole information paradox:
Geoff Penington, Stephen Shenker, Douglas Stanford, Zhenbin Yang, Replica wormholes and the black hole interior, J. High Energ. Phys. 2022 205 (2022) [doi:10.1007/JHEP05(2020)013, arXiv:1911.11977]
Ahmed Almheiri, Thomas Hartman, Juan Maldacena, Edgar Shaghoulian, Amirhossein Tajdini, Replica Wormholes and the Entropy of Hawking Radiation, J. High Energ. Phys. 2020 13 (2020) [doi:10.1007/JHEP05(2020)013, arXiv:1911.12333]
Review aimed at readers with minimal background:
See also:
Anna Karlsson, Concerns about the replica wormhole derivation of the island conjecture (arXiv:2101.05879)
Harvendra Singh, Islands and Icebergs contribute nothing to the Page curve (System with a symmetrical bath) [arXiv:2210.13970]
Argument that the would-be proof of the island conjecture secretly works only for massive gravity:
Hao Geng, Andreas Karch, Massive Islands, J. High Energ. Phys. 2020 121 (2020) [doi:10.1007/JHEP09(2020)121, arXiv:2006.02438]
Hao Geng, Andreas Karch, Carlos Perez-Pardavila, Suvrat Raju, Lisa Randall, Marcos Riojas, Sanjit Shashi, Inconsistency of islands in theories with long-range gravity, J. High Energ. Phys. 2022 182 (2022) [doi:10.1007/JHEP01(2022)182]
Hao Geng, Graviton Mass and Entanglement Islands in Low Spacetime Dimensions [arXiv:2312.13336]
reviewed in:
and discussion of what to do about this problem:
Claim that the whole argument relies on the false assumption that the split property holds for quantum gravity:
Review in:
Nirmalya Kajuri, Of Islands, Holograms and Saving Quantum Physics From a Black Hole Paradox, Science – The Wire (Nov 2022)
$[\ldots]$ a few sceptics have argued that while the calculations are correct, they don’t help resolve the black hole information-loss paradox. The troubles stem from the reservoir attached to the anti-de Sitter universe. The physicists who authored the island papers assumed that gravity stopped at the boundary of the anti-de Sitter space and didn’t enter the reservoir. This is not an innocuous assumption. $[\ldots]$ The key takeaway is that the island way to recover information and save unitarity works perfectly well – if you slightly modify Einstein’s theory of gravity. These criticisms have been around for some two years now, and physicists are yet to resolve them in print. $[\ldots]$ physicists continue to publish papers by the hundreds about the entanglement islands but few attempt to answer whether the islands are compatible with the Einsteinian gravity of our universe. $[\ldots]$
See also:
Saskia Demulder, Alessandra Gnecchi, Ioannis Lavdas, Dieter Lüst, Islands and Light Gravitons in type IIB String Theory [arXiv:2204.03669]
Emil Martinec: “Thus far, picturesque evocations of quantum wormholes remain largely just that – picturesque evocations.” (2nd Nov 2022)
Argument that discussion of the issue in the toy example of 2d JT gravity does not actually generalize to higher dimensions:
Debate between a proponent and a critic :
See also:
An argument that dual observables on black hole thermodynamics are generically given by single trace operators that evaluate to weight systems on chord diagrams (such as observables on SYK model-like systems)
(for more see at weight systems on chord diagrams in physics):
Last revised on April 18, 2023 at 07:25:34. See the history of this page for a list of all contributions to it.