Noncommutative BTZ Black Hole in Polar Coordinates

Details Noncommutative BTZ Black Hole in Polar Coordinates Noncommutative BTZ Black Hole in Polar Coordinates

2008-08-18

arxiv.org/abs/0808.2330v3

Class.Quant.Grav.26:185001,2009

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0264-9381/26/18/185001

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.

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