Electromagnetic fields in Schwarzschild and Reissner-Nordstr\"om geometry. Quantum corrections to the black hole entropy

TL;DR

This paper analyzes electromagnetic fields in Schwarzschild and Reissner-Nordström black hole geometries, deriving quantum corrections to black hole entropy using semi-classical methods and the brick-wall model.

Contribution

It presents a detailed calculation of quantum corrections to black hole entropy considering electromagnetic fields in charged black hole backgrounds.

Findings

Quantum corrections to entropy are computed.

Electromagnetic fields are described by scalar equations in these geometries.

First-order quantum effects on black hole entropy are quantified.

Abstract

Using standard coordinates, the Maxwell equations in the Reissner-Nordstr\"om geometry are written in terms of a couple of scalar fields satisfying Klein-Gordon like equations. The density of states is derived in the semi-classical approximation and the first quantum corrections to the black hole entropy is computed by using the brick-wall model.