Solving the Vlasov equation in general relativity

A new numerical method for determining the dynamical evolution of a collisionless system in full general relativity is developed. The method exploits Liouville's theorem to determine the evolution of the distribution function of matter in phase space directly. The distribution function is governed by the collisionless Boltzmann (Vlasov) equation coupled to Einstein's equations for the gravitational field. The method accurately tracks the increasingly complicated fine-grained structure developed by the distribution function due to phase mixing. It can be used to study Newtonian as well as fully relativistic systems. Applications include violent relaxation, the stability of relativistic star clusters, and the collapse of unstable relativistic star clusters to black holes. 51 refs