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

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.