Quadratic superconducting cosmic strings revisited

TL;DR

This paper revisits quadratic gravity models to find the most general superconducting cosmic string solutions by directly integrating field equations, revealing their uniqueness and differences from previous solutions.

Contribution

It derives the most general superconducting cosmic string solutions in quadratic gravity, demonstrating their uniqueness and global properties beyond perturbative methods.

Findings

Most general solutions are mathematically unique up to coordinate transformations.

Solutions are not globally equivalent to previous exact solutions due to Killing vector properties.

Direct integration avoids perturbative limitations in deriving solutions.

Abstract

It has been shown that 5-dimensional general relativity action extended by appropriate quadratic terms admits a singular superconducting cosmic string solution. We search for cosmic strings endowed with similar and extended physical properties by directly integrating the non-linear matrix field equations thus avoiding the perturbative approach by which we constructed the above-mentioned \textsl{exact} solution. The most general superconducting cosmic string, subject to some constraints, will be derived and shown to be mathematically \textsl{unique} up to linear coordinate transformations mixing its Killing vectors. The most general solution, however, is not globally equivalent to the old one due to the existence of Killing vectors with closed orbits.