  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.
