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=GM2) 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 cL=(12J)/(ℏ). 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 TL=(1)/(2π) and conjugate energy given by the zero mode generator, L0, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy Smicro=(2πJ)/(ℏ) for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy Smacro=(Area)/(4ℏG). 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 cL=(12J)/(ℏ), and, in particular, that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with cL∼2×1079.
- Publication:
-
Physical Review D
- Pub Date:
- December 2009
- DOI:
- 10.1103/PhysRevD.80.124008
- arXiv:
- arXiv:0809.4266
- Bibcode:
- 2009PhRvD..80l4008G
- Keywords:
-
- 04.60.-m;
- 04.70.Dy;
- Quantum gravity;
- Quantum aspects of black holes evaporation thermodynamics;
- High Energy Physics - Theory;
- Astrophysics;
- General Relativity and Quantum Cosmology
- E-Print:
- 21 pages, no figures