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. We formulate 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 we focus 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 less-than-or-equal-to 1 and neither a bang in the past nor a crunch in the future were not found. Our findings must have important consequences for any possible quantized version of such a system.