Charged rotating BTZ black holes in noncommutative space and torsion gravity

We consider charged rotating BTZ black holes in noncommutative space by use of Chern-Simons theory formulation of 2+1 dimensional gravity. The noncommutativity between the radial and the angle variables is introduced through the Seiberg-Witten map for gauge fields, and the deformed geometry to the first order in the noncommutative parameter is calculated. It is found that the deformation also induces nontrivial torsion, and the framework of Einstein-Cartan theory appears to be suitable to investigate the equations of motion. Though the deformation is indeed nontrivial, the deformed and the original Einstein equations are found to be related by a rather simple coordinate change.