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) × U(1, 1) noncommutative Chern–Simons theory using the Seiberg–Witten map. The Seiberg–Witten map is carried out in 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 nonrotating limit showing the effect of noncommutativity between the radial and angular coordinates.
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