Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes

TL;DR

This paper explores a non-canonical noncommutative extension of quantum gravity models to address black hole singularities, showing that such models can regularize the Kantowski-Sachs singularity and match thermodynamic properties with Hawking's predictions.

Contribution

It introduces a novel noncommutative algebra extension to the Wheeler-DeWitt equation, providing a new approach to black hole singularity resolution and thermodynamics.

Findings

Regularizes Kantowski-Sachs singularity via noncommutativity

Predicts vanishing probability near singularity, indicating singularity resolution

Matches black hole thermodynamics with Hawking values

Abstract

We consider a cosmological model based upon a non-canonical noncommutative extension of the Heisenberg-Weyl algebra to address the thermodynamical stability and the singularity problem of both the Schwarzschild and the Kantowski-Sachs black holes. The interior of the black hole is modelled by a noncommutative extension of the Wheeler-DeWitt equation. We compute the temperature and entropy of a Kantowski-Sachs black hole and compare our results with the Hawking values. Again, the noncommutativity in the momenta sector allows us to have a minimum in the potential, which is relevant in order to apply the Feynman-Hibbs procedure. For Kantowski-Sachs black holes, the same model is shown to generate a non-unitary dynamics, predicting vanishing total probability in the neighborhood of the singularity. This result effectively regularizes the Kantowski-Sachs singularity and generalizes a similar result, previously obtained for the case of Schwarzschild black hole.