Abstract
We consider noncommutative BTZ black hole solutions in two different coordinate systems, the polar and rectangular coordinates. The analysis is carried out by obtaining noncommutative solutions of U(1, 1) × U(1, 1) Chern-Simons theory on AdS3 in the two coordinate systems via the Seiberg-Witten map. This is based on the noncommutative extension of the equivalence between the classical BTZ solution and the solution of ordinary SU(1, 1) × SU(1, 1) Chern-Simons theory on AdS3. The obtained solutions in these noncommutative coordinate systems become different in the first order of the noncommutativity parameter θ.
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