Gravitating superconducting strings with timelike or spacelike currents

TL;DR

This paper numerically constructs and analyzes gravitating superconducting string solutions with timelike or spacelike currents, revealing new stable regions due to gravity and exploring their spacetime properties and particle dynamics.

Contribution

It introduces a numerical method to find gravitating superconducting string solutions with currents, showing gravity enables new stability regions and characterizing their spacetime structure.

Findings

Gravity induces new stable regions for superconducting strings.

Asymptotic spacetime matches Kasner metric with predictable relations.

Test particles can have bound orbits in Kasner spacetime.

Abstract

We construct gravitating superconducting string solutions of the U(1)_{local} x U(1)_{global} model solving the coupled system of Einstein and matter field equations numerically. We study the properties of these solutions in dependence on the ratio between the symmetry breaking scale and the Planck mass. Using the macroscopic stability conditions formulated by Carter, we observe that the coupling to gravity allows for a new stable region that is not present in the flat space-time limit. We match the asymptotic metric to the Kasner metric and show that the relations between the Kasner coefficients and the energy per unit length and tension suggested previously are well fulfilled for symmetry breaking scale much smaller than the Planck mass. We also study the solutions to the geodesic equation in this space-time. While geodesics in the exterior space-time of standard cosmic strings are just straight lines, test particles experience a force in a general Kasner space-time and as such bound orbits are possible.