Modified Dispersion Relations and Black Hole Entropy

TL;DR

This paper investigates how modified dispersion relations affect black hole entropy calculations, showing that the brick wall divergence can be eliminated by adjusting the density of states and radial coordinate dependence.

Contribution

It introduces a novel approach to remove the brick wall divergence in black hole entropy calculations using modified dispersion relations and specific radial coordinate functions.

Findings

Brick wall divergence can be eliminated with modified dispersion relations.

A specific radial coordinate dependence $r(E/E_P)$ is proposed.

Comparison with 't Hooft approach highlights differences in entropy computation.

Abstract

We compute the black hole entropy in the context of the Modified Dispersion Relations using the brick wall model. An explicit dependence of the radial coordinate approaching the horizon is shown to analyze the behavior of the divergence. We find that, due to the modification of the density of states, the brick wall can be eliminated. By assuming a specific form for the radial coordinate $r(E/E_{P}) $, we examine a possible candidate for $r(E/E_{P}) $. A comparison with the 't Hooft approach is presented.