Mathematical Sciences: Differential Geometry of Spacetimes

9310477哈里斯这项研究需要研究广义相对论中的类空超曲面。根据给定的观察者类别，这些表面可以表示在给定时刻的物理宇宙。研究人员希望调查是否所有这些在回火时空中的表面在拓扑上是相同的，并且是观测者时不变的。此外，他打算研究时空几何在曲率奇点方面崩溃的奇点。我们将利用伪黎曼几何中的技术。这项研究对于从理论上理解“黑洞”现象具有重要意义。

9310477 Harris The research entails the study of spacelike hypersurfaces in general relativity theory. These are surfaces which can represent the physical universe at a given instant of time according to a given class of observers. The investigator wishes to investigate whether all such surfaces in tempered spacetimes are topologically the same and are observer-time invariant. Also, he he intends studying singular points where the spacetime geometry collapses in terms of curvature singularities. Techniques from pseudo-Riemannian geometry will be exploited. This research is very pertinent to the theoretical understanding of `black-hole' phenomena.