Entropy of Reissner–Nordström–anti-de Sitter Black Hole

Abstract

By using the method of quantum statistics, we directly derive the partition function of bosonic and fermionic field in Reissner-Nordström-anti-de Sitter black hole and obtain the integral expression of black hole's entropy. It avoids the difficulty in solving the wave equation of various particles. Then via the improved brick-wall method, membrane model, we calculate the statistical entropy of a film with the thickness of (N − 1)ξ around the outside of horizon. In our result we can choose proper parameter in order to let the thickness of film tend to zero and have it approach the surface of horizon. Consequently, the entropy of black hole is proportional to the area of horizon. The stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, physics idea is clear; calculation is simple. We offer a new simple and direct way of calculating the entropy of different complicated black holes.