一类真空Einstein场方程时间周期解的性质

The Properties for a Kind of Time-Periodic Solutions of the Einstein’s Field Equations

摘要: 在广义相对论中，若存在有物理奇性的时间周期解，从而这个解为引力坍塌的最终状态给出了合理的解释。本文章研究了一类具有物理奇性的真空Einstein场方程的严格解，利用Maple得出该类解的Riemann曲率张量以及其模长，说明了它是一个带有物理奇性的时间周期解，这类特殊时间周期解刻画了一个带有时间周期物理奇性的时间周期宇宙。进而分析这类特殊解的Penrose图可以发现这类解都具有类似的物理性质。因为带有物理奇点的时间周期解可为引力坍缩最终状态给出合理的解释，所以这个时空可应用到现代宇宙学和广义相对论当中。

Abstract: In general relativity theory, the solution can provide rational explanation for the final state of gravitational collapse if it with physical singularity. In this paper, we study a kind of vacuum Ein-stein field equations time-periodic solution and its physical properties. We computed the Riemann curvature tensor and its length. We proved it’s a time-periodic solution with physical singularity which describes a time-period universe. Through analyzing the Penrose figure of this kind of solutions, we can be found this kind of solutions have similar Physical characters. Because of the time-periodic solutions with physical singularity can provide rational explanation for the final state of gravitational collapse, this space-time can apply to modern cosmology and general relativity.