Entropy of quantum-corrected black holes

TL;DR

This paper derives a general formula for the entropy of quantum-corrected black holes using the one-loop effective action and Wald's approach, confirming it for the Reissner-Nordstrom case and briefly discussing extremal black holes.

Contribution

It provides a new, general expression for the entropy of spherically symmetric quantum-corrected black holes based on the DeWitt-Schwinger expansion and Wald's method.

Findings

The derived entropy formula matches the first law integration for Reissner-Nordstrom black holes.

The approach is applicable to extremal quantum-corrected black holes.

The method confirms the consistency of quantum corrections with classical thermodynamics.

Abstract

The approximate renormalized one-loop effective action of the quantized massive scalar, spinor and vector field in a large mass limit, i.e., the lowest order of the DeWitt-Schwinger expansion involves the coincidence limit of the Hadamard-DeWitt coefficient a3. Building on this and using Wald's approach we shall construct the general expression describing entropy of the spherically-symmetric static black hole being the solution of the semi-classical field equations. For the concrete case of the quantum-corrected Reissner-Nordstrom black hole this result coincides, as expected, with the entropy obtained by integration of the first law of black hole thermodynamics with a suitable choice of the integration constant. The case of the extremal quantum corrected black hole is briefly considered.