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Noncommutative BTZ Black Hole in Polar Coordinates

By Ee Chang-young, Daeho Lee and Youngone Lee


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)×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 θ. 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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