Winding solutions for the two-particle system in gravity

We use a computer to follow the evolution of two gravitating particles in a (2 + 1)-dimensional closed universe. In a closed universe there is enough energy to produce a Gott-pair, i.e. a pair of particles with tachyonic centre of mass, from regular initial data. We study such a pair and find that they can wind around each other with ever increasing momentum. As was shown by 't Hooft, the universe must crunch before any closed timelike curve can be traversed. We study the two-particle system and quantize it, long before this crunch happens, in the high-momentum limit. We find that both the relevant configuration variable and its conjugate momentum become discretized.