Stability and global analysis of the Vlasov–Maxwell–Einstein system in astrophysical plasmas

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This paper provides an analysis of the relativistic Vlasov–Maxwell–Einstein (RVME) system, which models the dynamics of relativistic plasmas in the presence of strong gravitational fields. We establish the existence and uniqueness of global classical solutions using a fixed-point iteration method combined with a priori estimates. The stability of these solutions is analyzed with respect to small perturbations in the initial data to derive explicit stability bounds. The implications of our results are briefly discussed in the context of astrophysical scenarios, particularly focusing on the dynamics of plasmas near compact objects such as black holes and neutron stars.