The search for gravitational waves is already opening a new window on the universe and will allow new tests of our current theory of gravity. Sources of these waves are among the most extreme astrophysical systems imaginable the in the whole universe. They include binary systems of black holes and neutron stars, and stars orbiting and eventually spiralling into very large black holes. New methods of analysis will be developed to describe the dynamical evolution of these systems as they emit energy in the form of gravitational waves. Current descriptions of binary sources of gravitational waves are based on approximations of small speeds and weak gravitational fields. They begin to break down just when the physical system is at its most interesting, as the objects approach each other in their final stage of coalescence. New, accurate theoretical predictions will be developed, and will provide important guidance to experimental effort leading toward the detection of gravitational waves and the characterization of their sources. This research will have a broad impact upon our understanding of General Relativity to extreme astrophysical systems. Through the rigorous training of students, it will also have an impact upon science education, appreciation, and its public understanding, at all levels. People from all walks of life seem fascinated by physics examples involving black holes or cosmology. Four graduate students and an undergraduate are deeply involved in this project. They have the opportunity to develop sophisticated computational skills and to learn by the experience of doing. They will be able to follow other former students into the scientific research profession.
