The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle

TL;DR

This paper calculates the entropy of a 3D rotating noncommutative acoustic black hole using a generalized uncertainty principle, eliminating divergences without needing an ultraviolet cutoff or small mass approximation.

Contribution

It introduces a method to compute black hole entropy that avoids divergences and the small mass approximation by applying a generalized uncertainty principle.

Findings

Derived an area entropy for the noncommutative acoustic black hole.

Obtained a correction term related to the generalized uncertainty principle.

Eliminated the need for an ultraviolet cutoff in the entropy calculation.

Abstract

In this paper we investigate statistical entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when $\lambda$ introduced in the generalized uncertainty principle takes a specific value. However, in this method, it is not needed to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximation is not necessary in the original brick-wall model.