Abstract
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 (VP) system and the relativistic VP system into the discussion.
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