Black hole entropy without brick walls

TL;DR

This paper introduces a new equation of state density inspired by quantum gravity, which removes divergences in black hole entropy calculations without needing a cutoff, and confirms entropy proportionality to horizon area.

Contribution

It proposes a novel equation of state density that eliminates the brick wall divergence in black hole entropy calculations, providing a cutoff-free approach.

Findings

Divergence in black hole entropy is removed without cutoff.

Entropy remains proportional to horizon area.

No burst at the last emission stage of black holes.

Abstract

The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of a Schwarzshild black hole. When the new equation of state density is utilized to investigate the entropy of a scalar field outside the horizon of a static black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.