Particle decays and space-time kinematics in (2 + 1) gravity

We consider the properties of the space-time geometry in the presence of gravitating spinless particles in (2 + 1) dimensions. By using 't Hooft representation of three-dimensional space-time, we give a description of the decays of gravitating particles and derive the associated kinematic relations. The effects of gravity on the structure of the energy-momentum conservation law are discussed. We show that, for a set of spinless particles, the time evolution of the momenta can be described by means of a generalized space-time kinematics based on a particular representation of the braid group.