Black Holes and Phase Space Noncommutativity

We use the solutions of the noncommutative Wheeler-De Witt equation arising from a Kantowski-Sachs cosmological model to compute thermodynamic properties of the Schwarzschild black hole. We show that the noncommutativity in the momentum sector introduces a quadratic term in the potential function of the black hole minisuperspace model. This potential has a local minimum and thus the partition function can be computed by resorting to a saddle point evaluation in the neighbourhood of the minimum. The temperature and the entropy of the black hole are derived, and they have an explicit dependence on the inverse of the momentum noncommutative parameter, $\eta$. Moreover, we study the $t=r=0$ singularity in the noncommutative regime and show that in this case the wave function of the system vanishes in the neighbourhood of $t=r=0$.