发表机构
Tomsk State Pedagogical University (TSPU), Institute, of Scietific Research and Development; Tomsk State University of Control Systems and Radio Electronics (TUSUR)（托木斯克国立师范学院; 托木斯克国立控制系统与无线电电子大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对零齐性Petrov空间，利用三维齐性空间的规范标架构造度规与电磁场，求解可解运动群情形下Maxwell真空方程的全部精确解，并以波变量的任意函数显式表达，简化了Einstein-Maxwell方程的积分。
AI 中文摘要
本文考虑零齐性Petrov空间 $V^*_4(N)$。$V^*_4(N)$ 的几何由三维齐性黎曼空间 $V_3(N)$ 的几何决定，后者在三参数运动群 $G_3(N)$ 的作用下不变（$N$ 对应于Bianchi分类中的群编号）。利用空间 $V_3(N)$ 的规范标架，构造了空间 $V^*_4(N)$ 的度规张量以及不变电磁场的矢势分量。借助该标架，我们得到了仅包含群的结构常数、逆变度规张量和矢势的非完整分量及其对波变量的导数的Maxwell真空方程。对于可解运动群 $G_3(I)-G_3(VII)$ 的情形，找到了Maxwell真空方程的所有非等价精确解。本文获得的所有Maxwell真空方程的解均以波变量的任意独立函数的显式形式写出。因此，在积分Einstein-Maxwell方程时，只需考虑剩余的Einstein方程组，这些方程组可化为仅包含这些独立函数的常微分方程组。
英文摘要
Null homogeneous Petrov spaces $V^*_4(N)$ are considered. The geometry of $V^*_4(N)$ is determined by the geometry of the three-dimensional homogeneous Riemannian space $V_3(N)$, which is invariant under the action of the three-parameter motions group $G_3(N)$ ($N$ corresponds to the group number in the Bianchi classification). The canonical frame of the space $V_3(N)$ is used to construct the metric tensor of the space $V^*_4(N)$ and the components of the vector potential of the invariant electromagnetic field. Using this reper, we obtain Maxwell vacuum equations containing only the structure constants of the groups, the non-holonomic components of the contravariant metric tensor and vector potential, and their derivatives with respect to the wave variable. All non-equivalent exact solutions of Maxwell vacuum equations are found for the case of solvable motions groups $G_3(I)-G_3(VII)$. All solutions of Maxwell vacuum equations obtained in this article are written explicitly in terms of arbitrary independent functions of wave variable. Therefore, when integrating the Einstein-Maxwell equations, it has to consider only the remaining systems of Einstein equations which reduce to systems of ordinary differential equations that include only these independent functions.
Comments30 pages
