Kerr-CFT From Black-Hole Thermodynamics

TL;DR

This paper explores the connection between black hole thermodynamics and the Kerr/CFT correspondence by analyzing near-horizon geometries, asymptotic charges, and deriving entropy using conformal symmetry techniques.

Contribution

It demonstrates how near-horizon diffeomorphisms relate to asymptotic charges and reproduces black hole entropy via the Kerr/CFT framework.

Findings

Near-horizon diffeomorphisms can alter asymptotic charges.

The algebra of these diffeomorphisms yields a central charge.

Black hole entropy is obtained using Cardy's formula.

Abstract

We analyze the near-horizon limit of a general black hole with two commuting killing vector fields in the limit of zero temperature. We use black hole thermodynamics methods to relate asymptotic charges of the complete spacetime to those obtained in the near-horizon limit. We then show that some diffeomorphisms do alter asymptotic charges of the full spacetime, even though they are defined in the near horizon limit and, therefore, count black hole states. We show that these conditions are essentially the same as considered in the Kerr/CFT corresponcence. From the algebra constructed from these diffeomorphisms, one can extract its central charge and then obtain the black hole entropy by use of Cardy's formula.