The Entropy of a Quantum Field in a Charged Kerr Black Hole

Abstract

We calculate the entropies of the system of classical particles and a quantum scalar field by using the brick wall method in thermal bath in a charged Kerr black hole spacetime. Their leading terms at Hartle-Hawking temperature $T_H = κ/(2 π) $ are given by $ S_{cl} \approx N \ \ln \left( \frac{A_b}{ε^2} \right)$, and $S \approx N' \frac{A_H}{ε^2}$, where $A_b$ and $A_H$ are the area of the box and the horizon respectively.