  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 $U(1,1)\times U(1,1)$
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 $\theta$.
