Logarithmic correction to the entropy of extremal black holes in $\mathcal{N}=1$ Einstein-Maxwell supergravity

TL;DR

This paper calculates the logarithmic quantum corrections to the entropy of extremal black holes within a specific supergravity theory using heat kernel techniques, extending understanding of quantum effects on black hole entropy.

Contribution

It provides the first detailed computation of logarithmic entropy corrections for extremal black holes in non-minimally coupled  supergravity using heat kernel methods.

Findings

Logarithmic corrections to black hole entropy are explicitly computed.

Results apply to Kerr-Newman, Kerr, and Reissner-Nordstrf6m black holes.

The corrections depend on the non-minimal coupling in  supergravity.

Abstract

We study one-loop covariant effective action of \say{non-minimally coupled} $\mathcal{N}=1$, $d=4$ Einstein-Maxwell supergravity theory by heat kernel tool. By fluctuating the fields around the classical background, we study the functional determinant of Laplacian differential operator following Seeley-DeWitt technique of heat kernel expansion in proper time. We then compute the Seeley-DeWitt coefficients obtained through the expansion. A particular Seeley-DeWitt coefficient is used for determining the logarithmic correction to Bekenstein-Hawking entropy of extremal black holes using quantum entropy function formalism. We thus determine the logarithmic correction to the entropy of Kerr-Newman, Kerr and Reissner-Nordstr\"{o}m black holes in {\say{non-minimally coupled}} $\mathcal{N}=1$, $d=4$ Einstein-Maxwell supergravity theory.