Topics in Numerical Relativity

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9900644 HirschmannA study will be undertaken of the dynamics of gravitating systems in axisymmetry in which the gravitational field is very strong. In particular, dynamical situations will be studied in which the collapsing field configuration is strong enough to form a very small black hole. Advanced numerical code will be developed in order to investigate critical phenomena at the threshold of black hole formation in axisymmetric collapse. This model will be used to test the stability of exactly critical, self-similar solutions found previously in spherical symmetry. It will study the collapse of highly distorted scalar field and gravitational wave configurations. It will also begin an investigation of the role of rotation in critical gravitational collapse. Ongoing studies of critical phenomena in spherically symmetric collapse will also continue.This work will increase our understanding of realistic gravitational collapse within the context of general relativity. It will also shed light on other astrophysical processes in which the gravitational field plays a very significant role. This deeper and increased understanding of some of the strong-field, non-linear aspects of gravity has the potential to help in understanding some of the data which will come soon from gravitational wave detectors such as the LIGO project.