Integrability of the N-body problem in (2+1)-AdS gravity

TL;DR

This paper develops a formalism for analyzing the scattering of point sources in (2+1)-dimensional AdS gravity, revealing integrable structures and mapping complex dynamics to geodesic motion in a higher-dimensional space.

Contribution

It introduces a novel first order formalism that simplifies the two-body problem in (2+1) AdS gravity by transforming it into geodesic motion in an embedded Minkowskian space.

Findings

Two-body dynamics are characterized by two invariant masses.

Point sources follow geodesics in a three-dimensional hypersurface.

The formalism maps complex scattering to trivial motion via coordinate transformation.

Abstract

We derive a first order formalism for solving the scattering of point sources in (2+1) gravity with negative cosmological constant. We show that their physical motion can be mapped, with a polydromic coordinate transformation, to a trivial motion, in such a way that the point sources move as time-like geodesics (in the case of particles) or as space-like geodesics (in the case of BTZ black holes) of a three-dimensional hypersurface immersed in a four-dimensional Minkowskian space-time, and that the two-body dynamics is solved by two invariant masses, whose difference is simply related to the total angular momentum of the system.