Noncommutative BTZ Black Hole in Polar Coordinates

Abstract

Based on the equivalence between the three dimensional gravity and the Chern-Simons theory, we obtain a noncommutative BTZ black hole solution as a solution of $U(1,1)\times U(1,1)$ noncommutative Chern-Simons theory using the Seiberg-Witten map. The Seiberg-Witten map is carried out in a noncommutative polar coordinates whose commutation relation is equivalent to the usual canonical commutation relation in the rectangular coordinates up to first order in the noncommutativity parameter $\theta$. The solution exhibits a characteristic of noncommutative polar coordinates in such a way that the apparent horizon and the Killing horizon coincide only in the non-rotating limit showing the effect of noncommutativity between the radial and angular coordinates.

14 pages, V2: minor changes, v3: reduced for clarification, a reference added

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Cited by in corpus (19)

• Entanglement entropy of black holes
• Massive Vector Particles Tunneling From Noncommutative Charged Black Holes and its GUP-corrected Thermodynamics
• Thermodynamic stability of charged BTZ black holes: Ensemble dependency problem and its solution
• Gravitational Aharonov-Bohm effect due to noncommutative BTZ black hole
• The Ricci flow on noncommutative two-tori
• Noncommutative correction to the entropy of BTZ black hole with GUP
• Entropy and temperatures of Nariai black hole
• Gravity's Rainbow and Black Hole Entropy
• Analogy between the Schwarzschild solution in a noncommutative gauge theory and the Reissner-Nordström metric
• Charged rotating BTZ black holes in noncommutative spaces and torsion gravity
• Noncommutative Solitons of Gravity
• A Remark on Polar Noncommutativity
• Black Holes Thermodynamics in a new kind of Noncommutative Geometry
• Non-commutativity in polar coordinates
• $U(N)$ Yang-Mills in non-commutative space time
• The fuzzy BTZ
• Revision of the brick wall method for calculating the black hole thermodynamic quantities
• Dynamic noncommutative BTZ black holes
• Noncommutative BTZ Black Hole in Different Coordinates