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

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.