Studies of Singularities and Black Holes

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The singularity theorems tell us that singularities form in a large class of spacetimes, including the physically relevant cases of the big bang and of the gravitational collapse of a star to form a black hole. However, these theorems tell us very little about the nature of the singularities. For example, we would like to know for the entire class of incomplete observers, how the curvature behaves along their world lines and whether they can see the singularity before they hit it. Since we do not have the general solution of Einstein's equation in closed form, the PI intends to perform numerical studies of spacetimes with singularities to address these issues. The PI has already developed and successfully applied a fully 3-space dimensional vacuum code to study cosmological singularities and has found support for the BKL picture of oscillatory singularities. He plans to complement this with further work involving matter sources to test the idea that "matter doesn't matter" near the big bang. The PI also will study how coordinate conditions effect the numerical evolution of colliding black holes.