Electromagnetic fields in Schwarzschild and Reissner-Nordström geometry: Quantum corrections to the black hole entropy

Using standard coordinates, the Maxwell equations in 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 semiclassical approximation and the first quantum correction to black hole entropy is computed by using the brick-wall model.