A number of projects in theoretical gravitational physics will be completed. In the first set, issues pertaining to black holes will be analyzed using a new paradigm, introduced recently by Ashtekar's group. In particular, physical information will be extracted from numerical simulations of black hole mergers in regions where gravity is so strong that effects of Einstein's general relativity dominate. In the second set, mathematical issues pertaining to the structure and solutions of Einstein's general relativity will be resolved using ``Twistor theory'' introduced by Roger Penrose and developed by his research group. The third set contains a number of projects pertaining to quantum gravity, the theory that will unify general relativity with quantum physics. Suitable approximation methods will be developed by the research groups of Ashtekar and Pullin to better understand the structure of a quantum gravity theory, that is being developed by the PIs and others, and to make physical predictions which could be tested in the near future.
These projects interlink several fields: general relativity, computational physics, astrophysics, quantum theory and several branches of geometry. For example, the first set of projects is based on Einstein's equations of general relativity but the accurate estimates of the mass and spin of the final black hole and of the energy radiated in the process, obtained from them, will have impact on astrophysics in general and to gravitational wave physics in particular. The second set will use novel techniques from algebraic geometry to solve Einstein's equations. Unification of general relativity and quantum physics is perhaps the most outstanding open problem in fundamental physics today. The proposed projects in the third set combine sophisticated techniques from modern mathematics and theoretical physics to probe the nature of space-time geometry at the smallest scales conceivable today. Through his general relativity theory, Einstein proposed that geometry is a physical entity. Some of our projects are aimed at elevating Einstein's vision to the quantum world showing, in particular, that matter, radiation and geometry can be converted in to one another through quantum processes involving gravity. Other projects will use astronomical observations of gamma ray bursts from ongoing NASA missions to directly probe the ramifications of these novel quantum effects. This will be among the first systematic efforts at confronting the rather abstract quantum gravity theory with concrete experiments.
