A near-NHEK/CFT correspondence

TL;DR

This paper explores the near-horizon geometry of near-extremal Kerr black holes, revealing a dual conformal field theory description that reproduces black hole entropy via the Cardy formula.

Contribution

It establishes a near-NHEK/CFT correspondence by identifying boundary conditions and calculating central charges, linking black hole physics to conformal field theory.

Findings

Central charges c_L=12J/hbar and c_R=0 were derived.

The Cardy formula reproduces the Bekenstein-Hawking entropy.

The near-extremal Kerr black hole is holographically dual to a 2D CFT.

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 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.