Particle motion in weak relativistic gravitational fields

TL;DR

This paper derives the equations governing particle motion in weak relativistic gravitational fields, highlighting the significance of gravito-magnetic effects and enabling their inclusion in N-body simulations involving cosmic defects.

Contribution

It provides a detailed derivation of the geodesic equation in weak fields with relativistic sources, emphasizing the role of vector (gravito-magnetic) forces.

Findings

Vector (gravito-magnetic) forces are significant in particle motion.

Results recover known impulses from moving cosmic strings.

Framework can be integrated into N-body simulations for cosmic defects.

Abstract

We derive the geodesic equation of motion in the presence of weak gravitational fields produced by relativistic sources such as cosmic strings, decomposed into scalar, vector and tensor parts. We find that the vector (gravito-magnetic) force is an important contributor, and for non-relativistic particles we recover the well-known result for the impulse from a moving straight string. Our results can be straightforwardly incorporated into N-body simulations to allow for the presence of cosmic defects or other sources of weak gravitational fields.