Studies of Singularities

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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.