Abstract
A numerical relativity code designed to evolve rotating axisymmetric spacetimes is constructed. Both polarization states of gravitational radiation can be tracked. The source of the gravitational field is chosen to be a configuration of collisionless particles. The code is used to 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 $\frac{J}{{M}^{2}}<1$ collapse to black holes, while those with $\frac{J}{{M}^{2}}>1$ collapse to new equilibrium configurations.
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