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Title: The Kerr/CFT correspondence

Abstract

Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM{sup 2}) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c{sub L}=(12J/({Dirac_h}/2{pi})). This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T{sub L}=(1/2{pi}) and conjugate energy given by the zero mode generator, L{sub 0}, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S{sub micro}=(2{pi}J/({Dirac_h}/2{pi})) for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S{sub macro}=(Area/4({Dirac_h}/2{pi})G). The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c{sub L}=(12J/({Dirac_h}/2{pi})), and, in particular, that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c{sub L}{approx}2x10{sup 79}.

Authors:
 [1]; ; ;  [2]
  1. Laboratoire de Physique Theorique et Hautes Energies, Universite Pierre et Marie Curie-Paris 6, CNRS Boite 126, 4 Pl. Jussieu, 75252 Paris Cedex 05 (France)
  2. Center for the Fundamental Laws of Nature, Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138 (United States)
Publication Date:
OSTI Identifier:
21313600
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 80; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.80.124008; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANGULAR MOMENTUM; ASYMPTOTIC SOLUTIONS; BLACK HOLES; BOUNDARY CONDITIONS; CHIRALITY; CONFORMAL INVARIANCE; DENSITY MATRIX; ENTROPY; GESELLSCHAFT FUER ANLAGEN- UND REAKTORSICHERHEIT; KERR FIELD; MASS; QUANTUM FIELD THEORY; QUANTUM GRAVITY; SYMMETRY; TWO-DIMENSIONAL CALCULATIONS; UNITARITY; VACUUM STATES

Citation Formats

Guica, Monica, Hartman, Thomas, Wei, Song, and Strominger, Andrew. The Kerr/CFT correspondence. United States: N. p., 2009. Web. doi:10.1103/PHYSREVD.80.124008.
Guica, Monica, Hartman, Thomas, Wei, Song, & Strominger, Andrew. The Kerr/CFT correspondence. United States. https://doi.org/10.1103/PHYSREVD.80.124008
Guica, Monica, Hartman, Thomas, Wei, Song, and Strominger, Andrew. 2009. "The Kerr/CFT correspondence". United States. https://doi.org/10.1103/PHYSREVD.80.124008.
@article{osti_21313600,
title = {The Kerr/CFT correspondence},
author = {Guica, Monica and Hartman, Thomas and Wei, Song and Strominger, Andrew},
abstractNote = {Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM{sup 2}) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c{sub L}=(12J/({Dirac_h}/2{pi})). This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T{sub L}=(1/2{pi}) and conjugate energy given by the zero mode generator, L{sub 0}, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S{sub micro}=(2{pi}J/({Dirac_h}/2{pi})) for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S{sub macro}=(Area/4({Dirac_h}/2{pi})G). The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c{sub L}=(12J/({Dirac_h}/2{pi})), and, in particular, that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c{sub L}{approx}2x10{sup 79}.},
doi = {10.1103/PHYSREVD.80.124008},
url = {https://www.osti.gov/biblio/21313600}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 12,
volume = 80,
place = {United States},
year = {2009},
month = {12}
}