Thermodynamics and evaporation of a modified Schwarzschild black hole in a non--commutative gauge theory

In this work, we study the thermodynamic properties on a non–commutative background via gravitational gauge field potentials. This procedure is accomplished after contracting de Sitter (dS) group, $\mathrm{S}\mathrm{O}(4,1)$, with the Poincarè group, $\mathrm{I}\mathrm{S}\mathrm{O}(3,1)$. Particularly, we focus on a static spherically symmetric black hole. In this manner, we calculate the modified Hawking temperature and the other deformed thermal state quantities, namely, entropy, heat capacity, Helmholtz free energy and pressure. Finally, we also investigate the black hole evaporation process in such a context.