Solving The N-Body Problem in (2+1)-Gravity

TL;DR

This paper presents an explicit, non-perturbative solution for the N-body problem in (2+1)-dimensional gravity, addressing the metric and particle motion with novel coordinate mappings to handle multivaluedness.

Contribution

It introduces a method to construct single-valued solutions for multiple particles in (2+1)-gravity, including explicit solutions for two particles at any speed and small-speed solutions for many particles.

Findings

Explicit solutions for two-particle case at any speed

Solutions for multiple particles with small speeds

Detailed treatment of two and three-body cases

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.