A near-NHEK/CFT correspondence

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 x 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 non-vanishing and find the central charges c_L=12J/hbar and c_R=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 non-chiral two-dimensional conformal field theory.