Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes
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.
Keywords
Cite
@article{arxiv.1012.5523,
title = {Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes},
author = {Catarina Bastos and Orfeu Bertolami and Nuno Costa Dias and João Nuno Prata},
journal= {arXiv preprint arXiv:1012.5523},
year = {2011}
}
Comments
JHEP style, 14 pages, 2 figures