Einstein-Kepler problem in 2+1 dimensions

In (3+1)-dimensional general relativity, emission of gravitational
waves makes the dynamics of two compact objects a physically
interesting but mathematically difficult problem.
This talk discusses the motion of two point particles in Einstein's
theory in 2+1 spacetime dimensions, where gravitational waves are
absent. We formulate and solve the motion by anchoring the
two-particle system to an asymptotic (2+1)-dimensional infinity, in
analogy with the anchoring of an isolated (3+1)-dimensional
gravitating system to an asymptotic 3+1 Minkowski space. The reduced
phase space turns out to be analogous to the phase space of a
Newtonian two-body system in the centre-of-mass frame. Prospects for
quantisation are discussed.

(Joint work with Hans-Juergen Matschull [University of Mainz].)

Paper: Class. Quantum Grav. 17 (2000) 1847, e-print gr-qc/9908025.