The Kerr/CFT correspondence

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. 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=12π 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 for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy Smacro=Area4G. 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, and, in particular, that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with cL~2×10⁷⁹.