2008/09/25 by Monica Guica, Thomas Hartman, Wei Song +1 · 2 citations
Physics and Astronomy · #hep-th #astro-ph #gr-qc
paper · pdf · doi:10.1103/physrevd.80.124008
21 pages, no figures
arxiv created 2008/09/25 · arxiv updated 2013/05/29
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.