Extremal Kerr black hole entropy in Poincar\'e gauge theory

TL;DR

This paper investigates the near horizon symmetry of extremal Kerr black holes within Poincaré gauge theory, revealing a Virasoro algebra structure and deriving the black hole entropy using the Cardy formula.

Contribution

It demonstrates the realization of Virasoro algebra in Poincaré gauge theory for extremal Kerr black holes and computes the conformal entropy in this framework.

Findings

Virasoro algebra of canonical generators with horizon-dependent central charge

Conformal entropy matches the Bekenstein-Hawking entropy via Cardy formula

Analysis covers both Riemannian and teleparallel solutions

Abstract

We analyze the near horizon symmetry of the extremal Kerr black hole within the framework of Poincar\'e gauge theory (PG) for two important limiting cases: Riemannian and teleparallel solution. We show that the algebra of canonical generators is realized by Virasoro algebra, with central charge which depends on the black hole horizon radius . The conformal entropy of the black hole is obtained via Cardy formula.