Studies of Singularities

这个提议描述了广义相对论和弦理论中主要与奇点有关的一系列数值研究。拟议的研究的一部分是对没有对称性的一般时空的真空引力奇点进行数值探索。具体来说，PI提出了一个计划，数值研究广义相对论中空间依赖模型（缺乏对称性的模型）中的奇点。建议的研究的第二部分是应用PI的谐波规范数值相对论代码的两个黑洞的问题。拟议研究的第三部分与临界引力坍缩的进一步方面有关。PI打算在低能弦理论中进行相互作用膜的数值模拟。 PI还打算研究Ricci流，寻找临界崩溃的类似物。

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.