Central charge

TL;DR

This paper derives the central charge for Schwarzschild and extremal black holes using a CFT approach, revealing a universal form related to the black hole's intrinsic angular momentum.

Contribution

It introduces a universal expression for the central charge of 4D extremal black holes based on a CFT duality framework.

Findings

Central charge for Schwarzschild black hole is c=12J_in.

Temperature of the dual CFT is T=1/2π.

Universal form of central charge for extremal black holes.

Abstract

Proceeding in exactly the same way as in the derivation of the temperature of a dual CFT for the extremal black hole in the Kerr/CFT correspondence, it is found that the temperature of a chiral, dual CFT for the Schwarzschild black hole is $T=1/2\pi$. Comparing Cardy's formula with the Bekenstein-Hawking entropy and using $T$, it is found that the central charge for the Schwarzschild black hole is of the form $c=12J_{\rm in}$, where $J_{\rm in}$ is the intrinsic angular momentum of the black hole, $J_{\rm in}=A/8\pi G$. It is shown that the central charge for any four-dimensional (4D) extremal black hole is of the same form. The possible universality of this form is briefly discussed.