Price The relativistic astrophysics portion of the program consists of closely related projects, combining numerical and analytic approaches, all directed towards understanding black hole collisions. The motivation of this work comes from three directions. First, black hole collisions are an example of quintessentially nonlinear phenomena in relativistic gravitation. Second, black hole collisions are one of the most likely (and certainly the most exciting) sources of gravitational waves that will be detectable with forthcoming gravitational wave observatories. Third, black hole collisions are a testing ground for the development of numerical relativity on supercomputers. This work supports that development by providing tests of results, by pointing to interesting cases for computation, and by suggesting approximation schemes that may be useful in a computational approach.
Another set of problems under study aims at understanding the canonical quantization of Einstein's theory. Black holes are again at the center of attention, now at the submicroscopic scale. Specific projects include studying the effects of quantum gravity on formation of naked and covered singularities, mass inflation inside black holes, and horizon formation in the high-frequency limit in which zero-rest-mass fields can be described by null dust. Another main area of research is more fundamental and general; its goal is to clarify the connection among diffeomorphism invariance, constraints and observables. Specific projects include the representation of spacetime diffeomorphisms by canonical transformations and the study of Kretschmann-type observables in canonical gravity. ***
