Black holes and phasespace noncommutativity
Abstract
We use the solutions of the noncommutative WheelerDeWitt equation arising from a KantowskiSachs 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 neighborhood of the minimum. The thermodynamics of the black hole is derived and the corrections to the usual Hawking temperature and entropy exhibit a dependence on the momentum noncommutative parameter, η. 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 neighborhood of t=r=0.
 Publication:

Physical Review D
 Pub Date:
 December 2009
 DOI:
 10.1103/PhysRevD.80.124038
 arXiv:
 arXiv:0907.1818
 Bibcode:
 2009PhRvD..80l4038B
 Keywords:

 04.70.Dy;
 Quantum aspects of black holes evaporation thermodynamics;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 Astrophysics  High Energy Astrophysical Phenomena;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 Version to match the Physical Review D one