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

TL;DR

This paper computes logarithmic corrections to the entropy of various non-extremal black holes within a specific supergravity framework using Seeley-DeWitt coefficients, advancing understanding of quantum effects in black hole thermodynamics.

Contribution

It applies the field redefinition approach to calculate Seeley-DeWitt coefficients for non-minimal  supergravity and derives new logarithmic entropy corrections for several black hole types.

Findings

Logarithmic corrections are obtained for Kerr-Newman, Kerr, Reissner-Nordstrm, and Schwarzschild black holes.

The third Seeley-DeWitt coefficient is crucial for entropy correction calculations.

Results extend previous work to non-minimal  supergravity context.

Abstract

We reviewed the field redefinition approach of Seeley-DeWitt expansion for the determination of Seeley-DeWitt coefficients from arXiv:1505.01156. We apply this approach to compute the first three Seeley-DeWitt coefficients for \say{non-minimal} $\mathcal{N}=1$ Einstein-Maxwell supergravity in four dimensions. Finally, we use the third coefficient for the computation of the logarithmic corrections to the Bekenstein-Hawking entropy of non-extremal black holes following arXiv:1205.0971. We determine the logarithmic corrections for non-extremal Kerr-Newman, Kerr, Reissner-Nordstr\"{o}m and Schwarzschild black holes in \say{non-minimal} $\mathcal{N}=1$, $d=4$ Einstein-Maxwell supergravity.