On the Vlasov–Maxwell–Einstein equation and its non-relativistic and weakly relativistic analogues

In the present paper we consider the Lagrangian of gravity of general theory of relativity together with Lagrangian electromagnetism. From it derived equations of Vlasov type in general, non-relativistic and weakly relativistic limits. Expressions for the resulting corrections in the Poisson equation are proposed, which can contribute to the effective action of dark matter and dark energy.