(2+1)-Gravity with Moving Particles in an Instantaneous Gauge

TL;DR

This paper develops a conformal-like gauge for (2+1)-gravity with moving particles, providing explicit solutions for the metric and particle motion, including the two-body case at arbitrary speeds up to second order in mass.

Contribution

It introduces a regular gauge that allows instantaneous field propagation and separates field equations from particle motion in (2+1)-gravity with moving particles.

Findings

Derived explicit metric solutions for moving particles

Separated field equations from particle motion

Provided two-body solutions at arbitrary speeds up to second order

Abstract

By defining a regular gauge which is conformal-like and provides instantaneous field propagation, we investigate classical solutions of (2+1)-Gravity coupled to arbitrarily moving point-like particles. We show how to separate field equations from self-consistent motion and we provide a solution for the metric and the motion in the two-body case with arbitrary speed, up to second order in the mass parameters.