The Kerr/CFT correspondence

Journal Article · Tue Dec 15 00:00:00 EST 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.124008· OSTI ID:21313600

Guica, Monica ^[1]; Hartman, Thomas; Wei, Song; Strominger, Andrew ^[2]

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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)

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}.

• OSTI ID: 21313600
• Journal Information: Physical Review. D, Particles Fields, Vol. 80, Issue 12; Other Information: DOI: 10.1103/PhysRevD.80.124008; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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