Schwarzschild black hole thermodynamics in noncommutative spacetime with Gaussian, Levy and Cauchy mass distributions

In this paper, we employ the Hamilton-Jacobi method to investigate the thermodynamic properties of Schwarzschild black holes within a noncommutative spacetime framework. The analysis further explores the black holes behavior, by specifically examining the mass distribution from the perspective of non-Gaussian distributions. This work aims to enhance our understanding of black hole thermodynamics in noncommutative spacetime, recognizing the critical role this scale plays in connecting quantum mechanics and general relativity.