Classical Scattering in 2+1 Gravity with N Spinning Sources

TL;DR

This paper studies the classical behavior of spinning particles in 2+1 gravity using Chern-Simons theory, providing explicit solutions and analyzing scattering phenomena, including new results for massless particle interactions.

Contribution

It introduces explicit solutions for spinning sources in 2+1 Einstein-Cartan gravity and explores their scattering, extending previous work to include dynamical particles and massless limits.

Findings

Explicit solutions for dreibein and spin connection with spinning sources.

Gauge fixing ensures smooth metrics outside particles.

New results on scattering of two dynamical particles in the massless limit.

Abstract

The classical dynamics of N spinning point sources in 2+1 Einstein-Cartan gravity is considered. It corresponds to the ISO(2,1) Chern-Simons theory, in which the torsion source is restricted to its intrinsic spin part. A class of explicit solutions is found for the dreibein and the spin connection, which are torsionless in the spinless limit. By using the residual local Poincare' invariance of the solutions, we fix the gauge so that the metric is smooth outside the particles and satisfies proper asymptotic conditions at space and time infinity. We recover previous results for test bodies and find new ones for the scattering of two dynamical particles in the massless limit.