Stationary Solutions and Closed Time-Like Curve in 2+1 Dimensional Gravity

We give the general solution of the stationary problem of 2+1 dimensional gravity in 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).