Abstract

We consider a method for obtaining equations of the Hamiltonian dynamics for system of interacting massive charged particles using the general relativistic Einstein–Hilbert action. In the general relativistic case, Vlasov-type equations are derived in the nonrelativistic and weakly relativistic limits. Expressions are proposed for corrections to the Poisson equation, which can contribute to the effective action of dark matter and dark energy. In this case, an efficient approach to synchronizing the proper times of different particles of a many-particle system is proposed. Based on the obtained expressions for the action, we analyze the possibility of a composite structure of the cosmological term in the Einstein equations. Reduced Euler equations leading to the Milne–McCrea cosmological model are derived using a hydrodynamic substitution and are solved in the self-similar class.

中文翻译：

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弗拉索夫-麦克斯韦-爱因斯坦型方程及其结果。在天体物理问题中的应用

摘要

我们考虑一种使用广义相对论爱因斯坦-希尔伯特作用获得相互作用的大质量带电粒子系统的哈密顿动力学方程的方法。在一般相对论情况下，Vlasov 型方程是在非相对论和弱相对论极限下导出的。提出了对泊松方程进行修正的表达式，这有助于暗物质和暗能量的有效作用。在这种情况下，提出了一种同步多粒子系统中不同粒子的固有时间的有效方法。根据所获得的作用表达式，我们分析了爱因斯坦方程中宇宙项复合结构的可能性。使用流体动力学替代导出产生 Milne-McCrea 宇宙学模型的简化欧拉方程，并在自相似类中求解。