Entropy of a scalar field in a(3+1)-dimensional constant curvature black hole background

Abstract

We consider the thermodynamics of a minimally coupled massive scalar field in a $(3+1)$-dimensional constant curvature black hole background. The brick wall model of 't Hooft is used. When Scharzschild-like coordinates are used it is found that, apart from the usual radial brick wall cutoff parameter, an angular cutoff parameter is required to regularize the solution. The free energy of the scalar field is obtained through a counting of the states using the WKB approximation. It is found that the free energy and the entropy are logarithmically divergent in both cutoff parameters.