The evolution of gravitating point particles in 2+1 dimensions

The complete history of a set of classical gravitating point particles in 2+1 dimensions is considered, in the absence of a cosmological constant. The author formulates the equations of motion in terms of a time-dependent tessellation of Cauchy surfaces, of which a number of examples were run on a computer. In particular he focuses on the initial and final states. A given universe may either continue to expand for ever or shrink to a point in a final crunch, the latter being the rule rather than an exception. The past history may either be a 'big bang' or an infinitely large shrinking universe. Universes with g=0 may have both a bang in the past and a crunch in the future. Universes with g<or=1 and neither a bang in the past nor a crunch in the future were not found. His findings must have important consequences for any possible quantized version of such a system.