Stationary solutions and closed timelike curves in (2+1)-dimensional gravity

We give the general solution of the stationary problem of (2 + 1)-dimensional gravity in the presence of extended sources, also endowed with angular momentum. We solve explicitly the compact support property of the energy-momentum tensor and we apply the results to the study of closed time-like curves. In the case of rotational symmetry we prove that the weak-energy condition combined with the absence of closed time-like curves at space infinity prevents the existence of closed time-like curves everywhere in an open universe (conical space at infinity).