Geodesic motion in the space-time of a cosmic string

TL;DR

This paper analyzes the geodesic motion around an Abelian-Higgs cosmic string, revealing how particle trajectories depend on particle properties and fundamental mass ratios, with implications for light deflection and orbital shifts.

Contribution

It provides a detailed classification of particle orbits in the cosmic string spacetime and explores how mass ratios influence geodesic behavior and observable effects.

Findings

Bound orbits for massive particles occur only if Higgs mass is less than gauge boson mass.

Massless particles always follow escape trajectories.

Light deflection and perihelion shift depend on mass ratios and symmetry breaking scale.

Abstract

We study the geodesic equation in the space-time of an Abelian-Higgs string and discuss the motion of massless and massive test particles. The geodesics can be classified according to the particles energy, angular momentum and linear momentum along the string axis. We observe that bound orbits of massive particles are only possible if the Higgs boson mass is smaller than the gauge boson mass, while massless particles always move on escape orbits. Moreover, neither massive nor massless particles can ever reach the string axis for non-vanishing angular momentum. We also discuss the dependence of light deflection by a cosmic string as well as the perihelion shift of bound orbits of massive particles on the ratio between Higgs and gauge boson mass and the ratio between symmetry breaking scale and Planck mass, respectively.