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 the 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 conical singularity method.