Solving the N-body problem in (2+1) gravity Original Research Article

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 the particlesʹ momenta. The two- and three-body cases are treated in detail.