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).

中文翻译：

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Vlasov-Maxwell-Einstein 方程的流体力学结果及其宇宙学应用

摘要

本文提出并实施了一种基于广义希尔伯特-爱因斯坦-泡利作用的变化获得一组封闭的 Vlasov-Maxwell-Einstein 方程（及其弱相对论和非相对论类似物）的方法。该技术还可以根据粒子分布函数获得能量-动量张量的精确形式。在 Vlasov 方程中使用流体动力学代入，得到 Euler-Lamb 方程，可以将其转化为 Hamilton-Jacobi 方程的形式。展示了宇宙学类型的流体动力系统的精确解，并分析了它们的物理结果（包括 Milne-McCrea 模型的推广）。