A new non-commutative correction to the thermodynamics and evaporation of the Schwarzschild black hole in non-commutative gauge theory

Abstract

We investigate the modified thermodynamic properties of a deformed Schwarzschild black hole arising from new noncommutative corrections to the tetrad fields obtained through the Seiberg-Witten map. By deriving the corrected event horizon radius, we evaluate the corresponding thermodynamic quantities, including the Hawking temperature, entropy, heat capacity, Helmholtz free energy, and pressure. We also examine the evaporation process of the black hole within this noncommutative framework. The behavior of the heat capacity reveals a rich thermodynamic structure consisting of three distinct phases: two unstable phases with negative heat capacity, corresponding to a large black hole and a small black hole, separated by an intermediate stable phase with positive heat capacity. Our analysis also shows that the Schwarzschild black hole in noncommutative geometry possesses a finite lifetime that exceeds that of its classical counterpart, owing to the effective contribution of noncommutativity to the black hole mass. The noncommutative correction naturally introduces a fundamental length scale, Θ=1,6.10^-35 m, which is of the order of the Planck length.