Winding Solutions for the two Particle System in 2+1 Gravity

TL;DR

This paper investigates the dynamics of two gravitating particles in 2+1 dimensions, revealing winding solutions, the formation of a Gott-pair, and a quantization of key variables in a large universe setting.

Contribution

It introduces a novel numerical approach to analyze particle evolution in 2+1 gravity and demonstrates the quantization of configuration variables in this context.

Findings

Particles wind around each other indefinitely

Formation of a Gott-pair with tachyonic center of mass

Quantization of configuration variable and conjugate momentum

Abstract

Using a PASCAL program to follow the evolution of two gravitating particles in 2+1 dimensions we find solutions in which the particles wind around one another indefinitely. As their center of mass moves `tachyonic' they form a Gott-pair. To avoid unphysical boundary conditions we consider a large but closed universe. After the particles have evolved for some time their momenta have grown very large. In this limit we quantize the model and find that both the relevant configuration variable and its conjugate momentum become discrete.