INTEGRABILITY OF THE N-BODY PROBLEM IN (2+1)-AdS GRAVITY

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 timelike geodesics (in the case of particles) or as spacelike 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.