Black-Hole Dynamics and Gravitational Waves

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A theoretical and numerical study will be made of several problems in numerical relativity and gravitational wave physics. A numerical method will be developed to allow the calculation of wave fields that propagate in the vicinity of black holes. This method will focus on directly computing the spacetime metric, which is the object that describes a gravitational field. Related to this effort, a study will be made to determine optimal non-reflecting boundary conditions, for use in the above-mentioned numerical method and for use in more general numerical relativity calculations. A study will also be made of matched-filter techniques that can be applied in analyzing data from the LIGO detectors to search for merging binary stars which involvesignificant levels of spin (rotation) of the two stars.The development of a numerical method for computing the spacetime metric on a black hole background is important for several reasons. Such a method might be applied to calculate the gradual merger of a small black hole that is orbiting around a larger, rotating black hole. Mergers like this are potentially detectable events in LIGO and the proposed NASA/ESA LISA mission. Computation of waves on black hole backgrounds is also an important arena for testing the stability of numerical calculations, which is a considerable general concern in numerical relativity at present. Specification of non-reflective boundary conditions for such calculations is complicated by the curvature of space around black holes. Development of a more accurate non-reflecting condition is an important component to accurately computing gravitational waves and may be an important ingredient to stabilizing some numerical calculations. Existing techniques to search through LIGO data will not detect weak signals from some merging binaries which have significant individual stellar rotation rates. Including spin effects is straightforward but leads to a computationally prohibitive task. Thegoal will be to find a search technique that incorporates the essential aspects of spin while remaining computationally viable.