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By using the 't Hooft "brick wall" model and the Pauli-Villars regularizationscheme we calculate the statistical-mechanical entropy arising from theminimally coupled scalar fields which rotate with the azimuthal angularvelocity $\Omega_0=\Omega_H$ ($\Omega_H$ is the angular velocity of the blackhole horizon) in the general four-dimensional non-extreme stationaryaxisymmetric black hole space-time. We also show, for the Kerr-Newman and theEinstein-Maxwell dilaton-axion black holes, that the statistical-mechanicalentropy obtained from our derivation and the quantum thermodynamical entropy bythe conical singularity method are equivalent.Comment: 8 pages, Latex, nofigure, accepted by Phys. Rev.

Quantum entropy of a nonextreme stationary axisymmetric black hole due to a minimally coupled quantum scalar field