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