Quantum entropy of the general non-extreme stationary axisymmetric black hole due to minimally coupled quantum scalar field

Abstract

By using the 't Hooft "brick wall" model and the Pauli-Villars regularization scheme we calculate the statistical-mechanical entropy arising from the minimally coupled scalar fields which rotate with the azimuthal angular velocity ${\Omega }_0={\Omega }_H$ (${\Omega }_H$ is the angular velocity of the black hole horizon) in the general four-dimensional non-extreme stationary axisymmetric black hole space-time. We also show, for the Kerr-Newman and the Einstein-Maxwell dilaton-axion black holes, that the statistical-mechanical entropy obtained from our derivation and the quantum thermodynamical entropy by the conical singularity method are equivalent.

8 pages, Latex, nofigure, accepted by Phys. Rev. D

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