Noncommutative BTZ Black Hole and Discrete Time

Details Noncommutative BTZ Black Hole and Discrete Time Noncommutative BTZ Black Hole and Discrete Time

2006-11-22

arxiv.org/abs/hep-th/0611233v2

Class.Quant.Grav.24:1647-1656,2007

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

10.1088/0264-9381/24/6/017

We search for all Poisson brackets for the BTZ black hole which are consistent with the geometry of the commutative solution and are of lowest order in the embedding coordinates. For arbitrary values for the angular momentum we obtain two two-parameter families of contact structures. We obtain the symplectic leaves, which characterize the irreducible representations of the noncommutative theory. The requirement that they be invariant under the action of the isometry group restricts to $R\times S^1$ symplectic leaves, where $R$ is associated with the Schwarzschild time. Quantization may then lead to a discrete spectrum for the time operator.

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