Entropy of the nonminimally coupled quantum scalar fields in a stationary axisymmetric Einstein-Maxwell dilaton-axion black hole

The statistical-mechanical entropy of the stationary axisymmetric Einstein- Maxwell dilaton-axion black hole is investigated by using the "brick wall" model in which the original Dirichlet condition is replaced by a scattering ansatz for the field functions at the event horizon and regularized With t he Pauli-Villars scheme. It is also shown for the Kerr black hole, that the statistical-mechanical entropy obtained from our derivation coincides with the one-loop, correction to its thermodynamical entropy obtained by the co nical singularity method.