The generalized Friedmann model as a self-similar solution of Vlasov–Poisson equation system

We derive from the principle of least action (a slight generalization of the classical one) the right-hand sides of Maxwell and Einstein equations for a system on charged particles in the framework of the Vlasov–Maxwell–Einstein system of equations. The reduced Euler equations are derived using hydrodynamic substitution and are solved within the self-similar class, as a consequence of the Vlasov system of equations. The properties of the generalized non-relativistic Friedmann–Milne–McCrea model are analyzed in context of Gurzadyan’s theorem on the general function satisfying the equivalency of sphere’s and point mass’s gravity.