Relativistic stellar systems with rotation

We present a method for constructing equilibrium axisymmetric star clusters with net rotation in general relativity. The method yields a self-consistent numerical solution of the relativistic Vlasov equation coupled to Einstein's equations for the gravitational field. We demonstrate the method by constructing several equilibrium sequences. The nonrotating limiting members of one family are highly relativistic spherical polytropes and are known to be dynamically unstable. The rotating members are therefore interesting configurations for future exploration to see whether rotation stabilizes or destabilizes strong-field collisionless equilibria. We also construct models that are likely to be unstable but that have too much angular momentum to collapse to Kerr black holes. Their fate will also be interesting to determine when they are employed as initial data in a relativistic evolution code. Another family of clusters that we construct consists of highly relativistic rotating tori. No ergoregions were found in any of the models in the limited survey reported here.