Near-Extremal Kerr AdS2xS2 Solution and Black-Hole/Near-Horizion-CFT Duality

TL;DR

This paper explores the thermodynamics of near-extremal Kerr black holes using an AdS2/CFT1 framework, deriving entropy and temperature through asymptotic symmetries and quantum field analysis.

Contribution

It introduces a finite horizon shift in near-NHEK geometry enabling a Kaluza-Klein reduction and a CFT description that reproduces black hole entropy.

Findings

Reproduces Bekenstein-Hawking entropy via Cardy formula

Derives a Virasoro algebra with calculable central charge

Computes Hawking temperature from quantum flux analysis

Abstract

We study the thermodynamics of the near horizon of near extremal Kerr geometry (near-NHEK) within an AdS2/CFT1 correspondence. We do this by shifting the horizon by a general finite mass, which does not alter the geometry and the resulting solution is still diffeomorphic to NHEK, however it allows for a Robertson Wilczek two dimensional Kaluza-Klein reduction and the introduction of a finite regulator on the AdS2 boundary. The resulting asymptotic symmetry group of the two dimensional Kaluza-Klein reduction leads to a non-vanishing quantum conformal field theory on the respective AdS2 boundary. The s-wave contribution of the energy-momentum-tensor of the CFT, together with the asymptotic symmetries, generate a Virasoro algebra with calculable center and non-vanishing lowest Virasoro eigen-mode. The central charge and lowest eigen-mode reproduce the near-NHEK Bekenstein-Hawking entropy via the statistical Cardy Formula and our derived central charge agrees with the standard Kerr/CFT Correspondence. We also compute the Hawking temperature of the shifted near-NHEK by analyzing quantum holomorphic fluxes of the Robinson and Wilczek two dimensional analogue fields.