SOLVING EINSTEIN EQUATIONS FOR ROTATING SPACETIMES - EVOLUTION OF RELATIVISTIC STAR-CLUSTERS

A numerical relativity code designed to evolve rotating axisymmetric s pacetimes is constructed. Both polarization states of gravitational ra diation can be tracked. The source of the gravitational field is chose n to be a configuration of collisionless particles. The code is used t o evaluate the stability of polytropic and toroidal star clusters. The formation of Kerr black holes by the collapse of unstable clusters is demonstrated. Unstable clusters with J/M2 < 1 collapse to black holes , while those with J/M2 > 1 collapse to new equilibrium configurations .