Theoretical Investigations in Classical and Quantum Gravity

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A number of projects in theoretical gravitational physics will becompleted. In the first set, issues pertaining to black holes will beanalyzed using a new paradigm, introduced recently by Ashtekar'sgroup. In particular, physical information will be extracted fromnumerical simulations of black hole mergers in regions where gravityis so strong that effects of Einstein's general relativity dominate.In the second set, mathematical issues pertaining to the structure andsolutions of Einstein's general relativity will be resolved using``Twistor theory'' introduced by Roger Penrose and developed by hisresearch group. The third set contains a number of projects pertainingto quantum gravity, the theory that will unify general relativity withquantum physics. Suitable approximation methods will be developed bythe research groups of Ashtekar and Pullin to better understand thestructure of a quantum gravity theory, that is being developed by thePIs and others, and to make physical predictions which could be testedin the near future.These projects interlink several fields: general relativity,computational physics, astrophysics, quantum theory and severalbranches of geometry. For example, the first set of projects is basedon Einstein's equations of general relativity but the accurateestimates of the mass and spin of the final black hole and of theenergy radiated in the process, obtained from them, will have impacton astrophysics in general and to gravitational wave physics inparticular. The second set will use novel techniques from algebraicgeometry to solve Einstein's equations. Unification of generalrelativity and quantum physics is perhaps the most outstanding openproblem in fundamental physics today. The proposed projects in thethird set combine sophisticated techniques from modern mathematics andtheoretical physics to probe the nature of space-time geometry at thesmallest scales conceivable today. Through his general relativitytheory, Einstein proposed that geometry is a physical entity. Some ofour projects are aimed at elevating Einstein's vision to the quantumworld showing, in particular, that matter, radiation and geometry canbe converted in to one another through quantum processes involvinggravity. Other projects will use astronomical observations of gammaray bursts from ongoing NASA missions to directly probe theramifications of these novel quantum effects. This will be among thefirst systematic efforts at confronting the rather abstract quantumgravity theory with concrete experiments.