Thermodynamic Properties of Yukawa-Schwarzschild Black Hole in Non-commutative Gauge Gravity

In this paper we construct a non-commutative gauge theory for the deformed metric corresponding to the modified structure of a gravitational field in the case of Yukawa-Schwarzschild non-commutative space-time. The thermodynamic properties and corrections to the gravitational force on the horizon of a non-commutative Yukawa-Schwarzschild black hole are analysed.Comment: 12 pages, 4 figure

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

In this paper, we constructed the deformed Schwarzschild black hole in the non-commutative (NC) gauge theory of gravity. Where the singularity at the origin is shifted by the non-commutativity to the finite radius $r_h=2m$ and changed the spherical symmetry of the black hole to the ellipse symmetry (deformed the NC event horizon). The thermodynamics property of the NC black hole is analyzed. As a first step, we describe the Hawking temperature and the entropy of the NC Schwarzschild black hole, where the result shows a difference in the pole-equator temperature of the black hole, and give us a new scenario of the black hole evaporation. Our estimation for the NC parameter is close to the Planck scale $\Theta\approx2.257\times 10^{-35}m$. Then, the description of the ADM mass, the heat capacity, and the Gibbs free energy of the deformed black hole show the effect of the NC gauge theory on the thermodynamic stability and the phase transitions. Finally, we investigated the influence of the pressure of the black hole in the first law of thermodynamics on the stability and the phase transition of the Schwarzschild black hole in the NC spacetime, where the result shows that the NC parameter plays a similar role as the thermodynamical function and defined the critical point as the pressure in the modified first law of thermodynamics which means a second-order phase transition or a continuous one. The stability and the phase transition of the Schwarzschild black hole are affected by the non-commutativity