Studies of Singularities

这项提议描述了一系列主要与奇点有关的广义相对论和弦理论的数值研究。这项研究的一部分是对没有对称性的一般时空中真空引力奇异性的数值探索。具体地说，PI提出了一项计划，对广义相对论中空间相关模型(缺乏对称性的模型)中的奇点进行数值研究。研究的第二部分是将圆周率的调和规范数值相对论编码应用于两个黑洞问题。拟议研究的第三部分与临界引力坍塌的进一步方面有关。PI打算在低能弦理论中对相互作用的膜进行数值模拟。PI还打算研究利玛窦流动，寻找与临界崩塌类似的现象。

This proposal describes a set of numerical studies in general relativity and string theory related, primarily, to singularities. Part of the proposed research is the numerical exploration of the singularity in vacuum gravity for generic spacetimes with no symmetries. Specifically, the PI presents a plan to numerically investigate singularities in spatially dependent models in general relativity (models lacking symmetry). A second part of the proposed research is to apply the PI's harmonic gauge numerical relativity code to the two black hole problem. A third portion of the proposed research has to do with further aspects of critical gravitational collapse. The PI intends to perform numerical simulations of interacting branes in low energy string theory. The PI also intends to study Ricci flows, looking for analogs of critical collapse.