Stability and instability results for equilibria of a (relativistic) self-gravitating collisionless gas -- A review

We review stability and instability results for self-gravitating matter distributions, where the matter model is a collisionless gas as described by the Vlasov equation. The focus is on the general relativistic situation, i.e., on steady states of the Einstein-Vlasov system and their stability properties. In order to put things into perspective we include the Vlasov-Poisson system and the relativistic Vlasov-Poisson system into the discussion.