Generalized Einstein-Maxwell theory: Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and non-extremal black holes

TL;DR

This paper systematically computes logarithmic entropy corrections for Kerr-Newman black holes within a generalized Einstein-Maxwell framework, utilizing Seeley-DeWitt coefficients and extending results to supergravity theories.

Contribution

It provides a comprehensive manual for calculating Seeley-DeWitt coefficients and applies this to derive entropy corrections for various black holes, including supersymmetric cases.

Findings

Calculated first three Seeley-DeWitt coefficients for generalized Einstein-Maxwell theory.

Derived logarithmic entropy corrections for extremal and non-extremal black holes.

Reproduced entropy corrections for extremal black holes in $\ abla$-extended supergravity.

Abstract

We present a consolidated manual of Euclidean gravity approaches for finding the logarithmic corrections to the entropy of the full Kerr-Newman family of black holes in both extremal and non-extremal limits. Seeley-DeWitt coefficients for the quadratic fluctuations of a concern gravity theory appear to be the key ingredients in this manual. Following the manual, we calculate the first three Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and non-extremal black holes in a generalized Einstein-Maxwell theory minimally-coupled to additional massless scalar, vector, spin-1/2 Dirac and spin-3/2 Rarita-Schwinger fields. We finally employ the Seeley-DeWitt data to reproduce the logarithmic entropy corrections for extremal black holes in all $\mathcal{N} \geq 2$ Einstein-Maxwell supergravity via an alternative local supersymmetrization method.