Quantum Gravitational Corrections to the Entropy of a Reissner-Nordström Black Hole

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-Nordström (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.

18 pages. v3: corrected expression of functional derivative and numerical factors for entropy and pressure. Final version published as an erratum in Eur. Phys. J. C

References in corpus (4)

• Non-local quantum effects in cosmology 1: Quantum memory, non-local FLRW equations and singularity avoidance
• Quantum Gravitational Corrections to the Entropy of a Schwarzschild Black Hole
• Entropy of Reissner-Nordstrom Black Holes with Minimal Length Revisited
• Quantum Gravitational Corrections to a Star Metric and the Black Hole Limit

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