Thermodynamic Properties of Schwarzschild Black Hole in Non-Commutative Gauge Theory of Gravity

TL;DR

This paper explores how non-commutative gauge theory modifies the thermodynamic properties of Schwarzschild black holes, revealing effects like temperature regularization, a fundamental length scale, and phase transition behavior.

Contribution

It introduces a novel analysis of black hole thermodynamics within non-commutative gauge theory, highlighting new effects on evaporation, stability, and phase transitions.

Findings

Non-commutativity removes temperature divergence.

Discovery of a fundamental length scale at Planck length.

Identification of a second-order phase transition.

Abstract

In this paper, we used the non-commutative (NC) gauge theory of gravity to investigate the thermodynamic properties of a deformed Schwarzschild black hole (SBH). Our results present a new scenario of black hole evaporation. As a first step, we described the Arnowitt-Deser-Misner (ADM) mass, the Hawking temperature, and the entropy of NC SBH. The non-commutativity removes the divergence behavior of temperature, and the result shows a difference in the pole-equator temperature. These corrections also reveal a new fundamental length at the Planck scale order, $\Theta \approx 2.257 \times 10^{-35}\,m$. In the last stage of evaporation, the NC correction exposes a remnant entropy $\hat{S}_0$ of the NC SBH. Then, the description of the heat capacity and the Gibbs free energy of the deformed black hole shows the effect of the NC gauge theory on the thermodynamic stability and the phase transitions. Finally, we investigate the influence of the black hole pressure on the stability and the phase transition of SBH in NC spacetime. In this study, we found that the NC parameter plays a similar role to the thermodynamic variables. The results show a second-order phase transition of NC SBH.