Aspects of black hole entropy

TL;DR

This paper explores the relationship between entanglement entropy and the brick wall model in black hole physics, demonstrating their equivalence under certain conditions and analyzing the model's stability in rotating backgrounds.

Contribution

It shows that entanglement entropy reduces to the brick wall model at maximal entanglement and analyzes the model's stability near rotating black hole horizons.

Findings

Entanglement entropy reduces to the brick wall model at maximal entanglement.

The brick wall model remains well-defined in rotating backgrounds if the boundary is close to the horizon.

Scalar fields in Kerr backgrounds have complex-frequency modes, but stability is maintained near the horizon.

Abstract

There have been many attempts to understand the statistical origin of black-hole entropy. Among them, entanglement entropy and the brick wall model are strong candidates. In this paper, first, we show that the entanglement approach reduces to the brick wall model when we seek the maximal entanglement entropy. After that, the stability of the brick wall model is analyzed in a rotating background. It is shown that in the Kerr background without horizon but with an inner boundary a scalar field has complex-frequency modes and that, however, the imaginary part of the complex frequency can be small enough compared with the Hawking temperature if the inner boundary is sufficiently close to the horizon, say at a proper altitude of Planck scale. Hence, the brick wall model is well defined even in a rotating background if the inner boundary is sufficiently close to the horizon. These results strongly suggest that the entanglement approach is also well defined in a rotating background.