Noncommutative BTZ Black Hole and Discrete Time

Abstract

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.

10 pages

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• Noncommutative duality and fermionic quasinormal modes of the BTZ black hole
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Effects of Noncommutativity on the Black Hole Entropy
• The Ricci flow on noncommutative two-tori
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Exact Black Hole Solutions in Noncommutative Gravity
• Quantum statistics and noncommutative black holes
• Time Discretization From Noncommutativity
• Noncommutativity and logarithmic correction to the black hole entropy
• Noncommutative Corrections to the Robertson-Walker metric
• Field Theory on Curved Noncommutative Spacetimes
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• Exact solutions of noncommutative vacuum Einstein field equations and plane-fronted gravitational waves
• Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Double Quantization
• Noncommutative correction to the entropy of charged BTZ black hole
• Noncommutativity and the Weak Cosmic Censorship
• Charged rotating BTZ black holes in noncommutative spaces and torsion gravity
• Noncommutative Static Strings from Matrix Models
• Gravitational collapse of spherically symmetric stars in noncommutative general relativity
• Quantum space and quantum completeness
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• Projective module description of embedded noncommutative spaces
• Entropy of black holes, charged probes and noncommutative generalization
• Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes