空间变尺度因子球坐标系与四维时空度规

摘要

时空度规是广义相对论的一个基础性概念，是宇宙学和天体物理学建立模型的逻辑基础．将随时序参数变化的空间尺度因子函数引入相对论四维时空间隔模型，研究空间球对称形式的四维平直时空度规、Schwarzschild度规、Robertson-Walker（R．w）度规之间的变换条件．基于空间变尺度因子球坐标系的时空间隔，通过严格的计算，推导出R-w度规中与k=-4-1对应的尺度因子函数解析解，还推导出星球外非真空条件下的四维时空度规．提出了一种理解现代物理学非平直时空模型的新视角．%The time-space metric is a fundamental concept of general relativity, and it is the logical foundation of cosmology and astrophysics. A time-related space scale factor is introduced into a 4-dimensional time-space interval model. The transformations among the flat metric, the Schwarzschild metric and the Robertson-Walker （R-W） metric are obtained in spherical coordinate system. Based on the time-space interval of the time-related scale factor coordinate, the solutions of R-W metric with parameter k = 4-1 and the nonvacuum metric outside stars are deduced. A new point of view is advanced to comprehend the modem physical non-flat time-space.