Numerical Studies of Singularities and Black Holes

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This project will use computer simulations to explore the consequences of gravitational collapse and the formation of black holes and spacetime singularities. The small scale structure of general singularities will be studied in detail. In particular the suitability of such singularities as precursors for the initial singularity of the big bang will be explored. Simulations will also be done of the interior of a black hole to see whether the inner horizon of the black hole is replaced by a null singularity. Simulations will also be done of critical gravitational collapse and of gravitational collapse with a negative cosmological constant.The simulations of gravitational collapse as a possible precursor of the Big Bang are a promising approach to the question of "where did the universe come from?" Critical gravitational collapse is analogous to phase transitions in condensed matter physics and thus points to deep connections between two very different areas of physics. Gravitational collapse with a negative cosmological constant is connected through the so called AdS/CFT correspondence to such diverse physical systems as colliding heavy ion beams and high temperature superconductors.