Black Holes and Phase Space Noncommutativity

TL;DR

This paper investigates how phase space noncommutativity affects Schwarzschild black hole thermodynamics using a noncommutative Wheeler-De Witt approach, revealing modifications to temperature, entropy, and singularity behavior.

Contribution

It introduces a novel noncommutative minisuperspace model for black holes and computes thermodynamic properties incorporating momentum noncommutativity effects.

Findings

Black hole temperature and entropy depend explicitly on the noncommutative parameter η.

The potential in the model has a local minimum enabling saddle point approximation.

Wave function vanishes near the singularity in the noncommutative regime.

Abstract

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 $t=r=0$.