Conical geometry and quantum entropy of a charged Kerr black hole

TL;DR

This paper calculates the classical and quantum corrections to the entropy of a charged Kerr black hole using conical singularity methods, extending techniques from static black holes to rotating charged cases.

Contribution

It applies conical singularity techniques to derive quantum entropy corrections for a charged Kerr black hole, including the effects of rotation and charge.

Findings

Quantum corrections are obtained via heat kernel expansion.

Divergences in quantum corrections can be renormalized.

Conical singularities at the horizon are characterized for Kerr-Newman geometry.

Abstract

We apply the method of conical singularities to calculate the tree-level entropy and its one-loop quantum corrections for a charged Kerr black hole. The Euclidean geometry for the Kerr-Newman metric is considered. We show that for an arbitrary periodization in Euclidean space there exists a conical singularity at the horizon. Its $\delta$-function like curvatures are calculated and are shown to behave similar to the static case. The heat kernel expansion for a scalar field on this conical space background is derived and the (divergent) quantum correction to the entropy is obtained. It is argued that these divergences can be removed by renormalization of couplings in the tree-level gravitational action in a manner similar to that for a static black hole.