This project contains two components: (1) The astrophysical research focuses on a program to produce approximate gravitational waveforms to provide useful information to ongoing gravitational wave detection experiments on a faster time scale than that likely to be needed for an accurate numerical simulation. In their last few orbits of inspiral, and in their final plunge and merger, these binaries strongly curve spacetime and strongly emit gravitational waves. A complete understanding of this process, and of the gravitational waveforms produced, will require much further development of supercomputer evolution codes. The approach here is to use an approximation scheme for the gradual late-stage binary inspiral followed by supercomputer evolution for the final inward plunge and merger of the holes. The method exploits the fact that the spacetime of the gradual inspiral differs very little from that of a perfectly periodic binary. This gradual inspiral is therefore approximated by an exactly periodic orbit. These periodic orbits can be used to construct a quasiequilibrium sequence representing the gradual pre-plunge decrease in radius of the binary, and to give a good approximation to the corresponding gravitational waveform. (2) An outstanding problem in theoretical physics is how to reconcile the principles of quantum theory with those of general relativity. In general relativity, spacetime does not have any fixed structure which is not dynamical but governs dynamics from outside as an unmoved mover. On the other hand, quantum theory depends on such structures. This project views Einstein's theory as a model on which one can clarify how to quantize a system with no external structure without introducing an external structure. The first main theme here is that foliations can be viewed not as fixed elements but as free variables which help us to build phase space from spacetime foliation. The second main theme is more specific. A black hole is formed by a spherical collapse of quantum matter that produces quantum geometry without its own degrees of freedom will be studied. A mean geometry and its fluctuations will be determined, and a study will be made of how the radiation produced on this background differs from the thermal radiation fields.
At present, relativistic gravitation is of crucial interest both at the frontier of astrophysics and at the frontier of theoretical physics. This project contains research of both types. In addition to its broad impacts on the two frontiers of gravitational physics, this project will also provide broad theoretical training to postdoctoral researchers and students.
