The system of Vlasov-Maxwell-Einstein-type equations and its nonrelativistic and weak relativistic limits

We considered derivation of Vlasov-Einstein-Maxwell system of equations from the first principles, i.e. using classical Maxwell-Einstein-Hilbert action principle. We know many papers in which the theories indicated as Einstein-Vlasov, Vlasov-Maxwell-Einstein, Einstein-Maxwell-Boltzmann are discussed, and we discuss difficulties of usually used equations. We use another way of derivation and obtain an alternative version based on the generalized Fock-Weinberg form of equation of motion. © 2020 World Scientific Publishing Company.