Solving The N-Body Problem in (2+1)-Gravity
A. Bellini, M. Ciafaloni, P. Valtancoli
Abstract
We construct a non-perturbative, single-valued solution for the metric and the motion of N interacting particles in 2+1-Gravity. The solution is explicit for two particles with any speed and for any number of particles with small speed. It is based on a mapping from multivalued Minkowskian coordinates to single-valued ones, which solves the non-abelian monodromies due to particles' momenta. The two and three-body cases are treated in detail.
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