Entropies of the general nonextreme stationary axisymmetric black hole: Statistical mechanics and thermodynamics - art. no. 044016

Starting from the metric of the general nonextreme stationary axisymmetric black hole in four-dimensional spacetime, both statistical-mechanical and t hermodynamical entropies are studied. First, by means of the ''brick wall'' model in which the Dirichlet condition is replaced by a scattering ansatz for the field functions at the horizon and with Pauli-Villars regularizatio n scheme, an expression for the statistical-mechanical entropy arising from the nonminimally coupled scalar fields is obtained. Then, by using the con ical singularity method Mann and Solodukhin's result for the Kerr-Newman bl ack hole [Phys. Rev. D 54, 3932 (1996)] is extended to the general stationa ry black hole and the nonminimally coupled scalar field. We last show, by c omparing the two results, that the statistical-mechanical entropy and one-l oop correction to the thermodynamical entropy are equivalent for coupling x i less than or equal to 0. After renormalization, a relation between the tw o entropies is given.