Quantum Gravitational Corrections to the Entropy of a Reissner-Nordstr\"om Black Hole

TL;DR

This paper calculates quantum gravitational corrections to the entropy, temperature, and pressure of a non-extremal Reissner-Nordström black hole, extending previous work on Schwarzschild black holes by including charge effects.

Contribution

It generalizes prior calculations of quantum corrections to black hole entropy by including electric charge and analyzing the impact on the event horizon and thermodynamic properties.

Findings

Quantum corrections shift the classical event horizon position.

Corrections to entropy, temperature, and pressure are explicitly computed.

The study extends quantum gravity effects to charged black holes.

Abstract

Starting from an effective action for quantum gravity, we calculate the quantum gravitational corrections to the Wald entropy of a four dimensional non-extremal Reissner-Nordstr\"om (RN) black hole in the limit of small electric charge, generalising a previous calculation carried out by Calmet and Kuipers [1] for a Schwarzschild black hole. We show that, at second order in the Ricci curvature, the RN metric receives quantum corrections which shift the classical position of the event horizon. We apply the Wald entropy formula by integrating over the perimeter of the quantum corrected event horizon. We then compute the quantum gravitational corrections to the temperature and the pressure of the black hole.