arXiv 0705.29942007-05-26gr-qc

爱因斯坦方程的非相对论极限

Non-relativistic limit of the Einstein equation

Z. Ya. Turakulov

备注：: 8 pages

摘要：

在稳态和稳态轴对称时空的特殊情况下，完成了爱因斯坦方程到非相对论极限的过渡。为了这个目的，绝对空间和绝对时间的概念被引入，由于考虑中的时空的平稳性。在这种构造中，绝对时间被定义为时空上的函数$t$，使得$\prt_t$恰好是Killing向量，并且不同时刻的空间由表面$t=\con $表示。时空度规用三维空间的度规和两种势来表示，一种是牛顿引力势$Φ$，另一种是矢量势$\vec A$，它不同于经典电动力学中已知的矢量势。在$Φ/c^2$上的一级近似下，将$|\vec A|/c$ Einstein方程化为一个由这些函数组成的系统，其中左边是牛顿势的Laplacian、矢势的导数和空间曲率，右边是三维应力张量和质能密度。Subj-class：经典物理

英文摘要：

In particular cases of stationary and stationary axially symmetric space-time passage to non-relativistic limit of Einstein equation is completed. For this end the notions of absolute space and absolute time are introduced due to stationarity of the space-time under consideration. In this construction absolute time is defined as a function $t$ on the space-time such that $\prt_t$ is exactly the Killing vector and the space at different moments is presented by the surfaces $t=\con $. The space-time metric is expressed in terms of metric of the 3-space and two potentials one of which is exactly Newtonian gravitational potential $Φ$, another is vector potential $\vec A$ which, however, differs from vector potential known in classical electrodynamics. In the first-order approximation on $Φ/c^2$, $|\vec A|/c$ Einstein equation is reduced to a system for these functions in which left-hand sides contain Laplacian of the Newtonian potential, derivatives of the vector potential and curvature of the space and the right-hand sides do 3-dimensional stress tensor and densities of mass and energy. Subj-class: Classical Physics

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