Chern-Simons formulation of noncommutative gravity in three dimensions

We formulate noncommutative three-dimensional (3D) gravity by making use of its connection with 3D Chern-Simons theory. In the Euclidean sector, we consider the topology T²×R and show that the 3D black hole solves the noncommutative equations. We then consider the black hole on a constant U(1) background and show that the black hole charges (mass and angular momentum) are modified by the presence of this background.