The Entropy of a Quantum Field in a Charged Kerr Black Hole

TL;DR

This paper computes the entropy of classical particles and a quantum scalar field in a charged Kerr black hole spacetime using the brick wall method, revealing area-dependent leading terms at the Hartle-Hawking temperature.

Contribution

It provides explicit calculations of entropy contributions for quantum fields in a charged Kerr black hole, extending the brick wall method to this specific spacetime.

Findings

Classical particle entropy scales with the logarithm of the box area.

Quantum scalar field entropy is proportional to the horizon area.

Leading terms are derived at the Hartle-Hawking temperature.

Abstract

We calculate the entropies of the system of classical particles and a quantum scalar field by using the brick wall method in thermal bath in a charged Kerr black hole spacetime. Their leading terms at Hartle-Hawking temperature $T_H = \kappa/(2 \pi) $ are given by $ S_{cl} \approx N \ \ln \left( \frac{A_b}{\epsilon^2} \right)$, and $S \approx N' \frac{A_H}{\epsilon^2}$, where $A_b$ and $A_H$ are the area of the box and the horizon respectively.