Statistical entropy of a rotating higher-dimensional black hole

Abstract

By using the method of quantum statistics, we directly derive the partition function of the bosonic and the fermionic fields in the rotating (4 + n)-dimensional black hole and obtain an integral expression for the black hole's entropy. Then, via the improved brick-wall method, the membrane model, we obtain the statistical entropy of the black hole and find that we can choose a proper parameter in order to let the thickness of the film tend to zero and have it approach the surface of the horizon. Consequently, the entropy of the black hole is proportional to the area of the horizon. In our result, we also take the spinning degeneracy of various particles into consideration. The stripped term and the approximation taken in the original brick-wall method no longer exist. In the whole process, physics is clear, and the calculation is simple. We offer a new simple and direct way of calculating the entropy of the rotating higher-dimensional black holes.