Two Body Dynamics in General Relativity

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The dynamics of the relativistic two-body problem will be studied inthe limit where one of the bodies is very much more massive than theother. The extreme mass ratio is amenable to analytic treatment, andcan be used to describe a neutron star or similar object interactingwith a super-massive galactic black hole. The primary questions to beaddressed concern the dynamical stability of the orbits and thetransition from inspiral to plunge. This should shed light on ourability to extract information from the gravitational waves emittedduring the final stages of the orbital evolution. A variety of newand existing techniques will be developed and applied.The evolution of two masses under their mutual gravitational attractionis a major outstanding problem in classical general relativity. It hasa direct bearing on the observational program of the Laser InterferometerGravitational wave Observatory (LIGO). The possibly that the orbitalevolution is effectively chaotic has a number of interesting theoreticaland observational consequences.