Noncommutative correction to the entropy of BTZ black hole with GUP

TL;DR

This paper explores how noncommutativity and quantum effects, including GUP, modify the entropy and temperature of BTZ black holes, revealing logarithmic entropy corrections and stability insights.

Contribution

It introduces a combined analysis of noncommutative geometry and GUP effects on BTZ black hole thermodynamics using tunneling formalism.

Findings

Logarithmic corrections to black hole entropy due to noncommutativity and GUP.

Modified specific heat capacity indicating stability changes.

Application of Hamilton-Jacobi and WKB methods to derive Hawking radiation.

Abstract

We investigate the effect of noncommutativity and quantum corrections to the temperature and entropy of a BTZ black hole based on a Lorentzian distribution with the generalized uncertainty principle (GUP). To determine the Hawking radiation in the tunneling formalism we apply the Hamilton-Jacobi method by using the Wentzel-Kramers-Brillouin (WKB) approach. In the present study we have obtained logarithmic corrections to entropy due to the effect of noncommutativity and GUP. We also address the issue concerning stability of the non-commutative BTZ black hole by investigating its modified specific heat capacity.