Noncommutative formulation of Schwarzschild black hole and its physical properties

In this paper, we study the effects of noncommutativity on solutions and the thermodynamic properties of a Schwarzschild black hole. Such noncommutativity is presented in the presence of the smeared Gaussian distribution mass and radius densities. We also examine the phase transition of our system by studying local and global stability. Our idea is a generalisation of noncommutative black holes, where we introduce the noncommutativity together with the radius coordinate and the source of matter.