Collisions of relativistic clusters and the formation of black holes

We perform numerical simulations of head-on collisions of relativistic clusters. The cluster particles interact only gravitationally, and so satisfy the collisionless Boltzmann equation in general relativity. We construct and follow the evolution of three classes of initial configurations: spheres of particles at rest; spheres of particles boosted towards each other; and spheres of particles in circular orbits about their respective centers. In the first two cases, the spheres implode towards their centers and may form black holes before colliding. These scenarios thus can be used to study the head-on collision of two black holes. In the third case the clusters are initially in equilibrium and cannot implode. In this case collision from rest leads either to coalescence and virialization, or collapse to a black hole. This scenario is the collisionless analog of colliding neutron stars in relativistic hydrodynamics.