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

TL;DR

This paper calculates the quantum entropy of rotating black holes using the 't Hooft brick wall model and shows equivalence with thermodynamic entropy for specific black hole types.

Contribution

It extends the calculation of quantum entropy to general non-extreme stationary axisymmetric black holes and compares methods for Kerr-Newman and Einstein-Maxwell dilaton-axion black holes.

Findings

Quantum entropy matches thermodynamic entropy for Kerr-Newman black holes.

The 't Hooft brick wall model and conical singularity method yield equivalent results.

Entropy calculation applies to rotating black holes with scalar fields.

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.