Dolan, B.P. and Gupta, Kumar S. and Stern, A.
Noncommutative BTZ Black Hole and Discrete Time.
Classical and Quantum Gravity, 24.
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 × S1 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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