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

Abstract

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.