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 nearhorizon quantum states can be identified with those of (a chiral half of) a twodimensional conformal field theory (CFT). Moreover, in the extreme limit, the FrolovThorne 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 BekensteinHawking 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 twodimensional conformal field theory with central charge c{sub L}=(12J/({Dirac_h}/2{pi})), and, in particular, that the nearextreme black hole GRS 1915+105 is approximately dual to a CFT with c{sub L}{approx}2x10{sup 79}.
 Authors:

 Laboratoire de Physique Theorique et Hautes Energies, Universite Pierre et Marie CurieParis 6, CNRS Boite 126, 4 Pl. Jussieu, 75252 Paris Cedex 05 (France)
 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 05562821
 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; TWODIMENSIONAL 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 nearhorizon quantum states can be identified with those of (a chiral half of) a twodimensional conformal field theory (CFT). Moreover, in the extreme limit, the FrolovThorne 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 BekensteinHawking 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 twodimensional conformal field theory with central charge c{sub L}=(12J/({Dirac_h}/2{pi})), and, in particular, that the nearextreme 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 = {05562821},
number = 12,
volume = 80,
place = {United States},
year = {2009},
month = {12}
}