抛物线坐标系及其度规、仿射联络

PARABOLA COORDINATE SYSTEM AND ITS RULE OF METRIC,AFFINE CONNECTION

抛物线坐标系是一种特殊的坐标系,对于静止质量类似于Coulomb势对称分布的物质,运用该坐标系有助于获得广义相对论时空下爱因斯坦引力场方程的近似解甚至解析解。本文详细地描述了它的坐标变量、坐标面及线元、体元,推导了它的度规及仿射联络,为求得爱因斯坦引力场方程的近似解甚至解析解提供工具准备。

Parabola coordinate system is a special coordinate system. According to the material whose static mass distribute symmetrically similar to the Coulomb potential, it is helpful to utilize the coordinate system to obtain the approximate solution, even the analytic solution of the Einstein gravitational field equation under the general theory of relativity. Furthermore, we describe its coordinate variable, coordinate surface, line element and body element. Finally, we deduce its rule of metric and affine connection and provide the tools for obtaining the approximate solution, even the analytic solution of the Einstein gravitational field equation.