2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215520We 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 $U(1,1)\times U(1,1)$ Chern-Simons theory on $AdS_3$ 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 $SU(1,1)\times SU(1,1)$ Chern-Simons theory on $AdS_3$. The obtained solutions in these noncommutative coordinate systems become different in the first order of the noncommutativity parameter $θ$.6 pages, Talk given at CosPA2008, October 2008High Energy Physics - Theorytext