On Derivation of Vlasov–Maxwell–Einstein Equations from the Principle of Least Action, the Hamilton–Jacobi Method, and the Milne–McCrea Model

V. V. Vedenyapin^a^,*

^aFederal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

Correspondence to: *e-mail: vicveden@yahoo.com

Received 11 November, 2023

Abstract— In classical texts equations for gravitation and electromagnetic fields are proposed without deriving their right-hand sides [1–4]. In this paper, we derive the right-hand sides and analyze the energy–momentum tensor in the framework of Vlasov–Maxwell–Einstein equations and Milne–McCrea models. New models of accelerated expansion of the Universe without Einstein’s lambda are proposed.

Keywords: Vlasov equation, Vlasov–Einstein equation, Vlasov–Maxwell equation, Vlasov–Poisson equation

DOI: 10.1134/S1064562424701692