Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory

TL;DR

This paper calculates the logarithmic correction to the entropy of extremal Kerr-Newman black holes using heat kernel expansion techniques in Einstein-Maxwell theory, providing insights into quantum gravity effects.

Contribution

It introduces a novel computation of the second Seely-DeWitt coefficient for Einstein-Maxwell theory in arbitrary backgrounds, enabling precise entropy corrections.

Findings

Logarithmic correction to extremal Kerr-Newman black hole entropy derived.

Second Seely-DeWitt coefficient computed for Einstein-Maxwell kinetic operators.

Method applicable to other black hole solutions and background fields.

Abstract

We compute the second Seely-DeWitt coefficient of the kinetic operator of the metric and gauge fields in Einstein-Maxwell theory in an arbitrary background field configuration. We then use this result to compute the logarithmic correction to the entropy of an extremal Kerr-Newmann black hole.