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

TL;DR

This review discusses the stability and instability of steady states in self-gravitating collisionless gases, focusing on the Einstein-Vlasov system and including related non-relativistic models.

Contribution

It provides a comprehensive overview of stability results for relativistic and non-relativistic self-gravitating collisionless gases, highlighting recent advances and open problems.

Findings

Stability criteria for Einstein-Vlasov steady states

Instability mechanisms identified in relativistic models

Comparison between relativistic and non-relativistic systems

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 system and the relativistic Vlasov-Poisson system into the discussion.