Hydrodynamic Consequences of Vlasov–Maxwell–Einstein Equations and Their Cosmological Applications

Abstract

The paper proposes and implements a method of obtaining a closed set of Vlasov–Maxwell–Einstein equations (and its weakly relativistic and nonrelativistic analogues) based on variation of the generalized Hilbert–Einstein–Pauli action. This technique also makes it possible to obtain the exact form of the energy-momentum tensor in terms of particle distribution functions. Using a hydrodynamic substitution in the Vlasov equation, the Euler–Lamb equations are obtained, which can be transformed to the form of Hamilton–Jacobi equations. Exact solutions of cosmological type of the hydrodynamic system are demonstrated, and their physical consequences are analyzed (including a generalization of the Milne–McCrea model).