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^{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_{L}=(12J)/(ℏ). 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_{L}=(1)/(2π) and conjugate energy given by the zero mode generator, L_{0}, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S_{micro}=(2πJ)/(ℏ) for the CFT, which reproduces the macroscopic BekensteinHawking entropy S_{macro}=(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 twodimensional conformal field theory with central charge c_{L}=(12J)/(ℏ), and, in particular, that the nearextreme black hole GRS 1915+105 is approximately dual to a CFT with c_{L}̃2×10^{79}.
 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
 EPrint:
 21 pages, no figures