Abstract:In this paper we study the effects of noncommutative phase space deformations on the Schwarzschild black hole. This idea has been previously studied in Friedmann-Robertson-Walker (FRW) cosmology, where this "noncommutativity" provides a simple mechanism that can explain the origin of the cosmological constant. In this paper, we obtain the same relationship between the cosmological constant and the deformation parameter that appears in deformed phase space cosmology, but in the context of the deformed phase space black holes. This was achieved by comparing the entropy of the deformed Schwarzschild black hole with the entropy of the Schwarzschild-de Sitter black hole.

Abstract:The thermodynamic formalism for rotating black holes, characterized by noncommutative and quantum corrections, is constructed. From a fundamental thermodynamic relation, the equations of state and thermodynamic response functions are explicitly given, and the effect of noncommutativity and quantum correction is discussed. It is shown that the well-known divergence exhibited in specific heat is not removed by any of these corrections. However, regions of thermodynamic stability are affected by noncommutativity, increasing the available states for which some thermodynamic stability conditions are satisfied.

We study some consequences of a wave packet resulting as a solution in a class of Supersymmetric Wheeler–DeWitt equation in Kantowski–Sachs minisuperspace. As a result of our analysis, we show that the Supersymmetric noncommutative proposal can modify significantly the universe evolution. The volume expansion, the shear and the characteristic volume are calculated explicit.