ON THE DYNAMICS OF A CLASS OF EINSTEIN–VLASOV SHELLS

Abstract

The Einstein–Vlasov equations govern the dynamics of systems of self-gravitating collisionless particles in the framework of general relativity. Here we review some recent results obtained by restricting to spherically symmetric systems and imposing the simplifying restrictions that the conserved angular momentum of the particles can take values only on a discrete, finite set. The first set of results is restricted to the existence of thin shells, their dynamics and stability. A second set is concerned with the existence of thick shells satisfying the same restrictions and the conditions under which they admit, in general, a thin shell limit. In a related result it is shown that the so called Einstein shells have a unique thin shell limit where the particle's angular momentum has a continuous distribution.