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We consider charged rotating BTZ black holes in noncommutative space by useof Chern-Simons theory formulation of $2+1$ dimensional gravity. Thenoncommutativity between the radial and the angular variables is introducedthrough the Seiberg-Witten map for gauge fields, and the deformed geometry tothe first order in the noncommutative parameter is derived. It is found thatthe deformation also induces nontrivial torsion, and the Einstein-Cartan theoryappears to be a suitable framework to investigate the equations of motion.Though the deformation is indeed nontrivial, the deformed and the originalEinstein equations are found to be related by a rather simple coordinatetransformation.

Charged rotating BTZ black holes in noncommutative spaces and torsion gravity