The Kerr/CFT Correspondence

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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=1/2πand 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 / 4ℏ 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 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.