A NEAR-NHEK/CFT CORRESPONDENCE

Abstract

We consider excitations around the recently introduced near-NHEK metric describing the near-horizon geometry of the near-extremal four-dimensional Kerr black hole. This geometry has a U (1)L × U (1)R isometry group which can be enhanced to a pair of commuting Virasoro algebras. We present boundary conditions for which the conserved charges of the corresponding asymptotic symmetries are well defined and nonvanishing and find the central charges cL = 12J/ℏ and cR = 0 where J is the angular momentum of the black hole. Applying the Cardy formula reproduces the Bekenstein–Hawking entropy of the black hole. This suggests that the near-extremal Kerr black hole is holographically dual to a nonchiral two-dimensional conformal field theory.