CLASSICAL SCATTERING IN 2+1 GRAVITY WITH N-POINT SOURCES

The classical dynamics of N point sources in three-dimensional gravity is considered. An explicit solution is found in the first-order formalism, where the dreibein and the spin connection correspond to a Chern-Simons gauge field on the Poincare group. If we are not interested in a smooth metric, as in the gauge theory, such a solution exists for arbitrary trajectories and conventional scattering is not defined. Only particle exchanges are meaningful. and are described by the braid group acting on the holonomies of the gauge field. On the other hand, the metric in the Einstein theory must be smooth and invertible, outside the particle trajectories, and fulfil proper asymptotic conditions. We argue that these requirements constrain the asymptotic motion of the particles, so that the two-body scattering problem is well defined. We determine the scattering angle in some special limits and we argue its exact form in the massless case.