Complete Classification of the String-like Solutions of the Gravitating Abelian Higgs Model

TL;DR

This paper provides a comprehensive classification of string-like solutions in the gravitating Abelian Higgs model, identifying distinct solution regions with different asymptotic behaviors and a boundary characterized by maximal angular deficit.

Contribution

It offers a complete classification of solutions, delineating the parameter space into regions with unique asymptotic properties and identifying the boundary curve.

Findings

Identification of two main regions in the parameter space.

Existence of solutions with asymptotically conic and Melvin-like behaviors.

Boundary characterized by maximal angular deficit of 2π.

Abstract

The static cylindrically symmetric solutions of the gravitating Abelian Higgs model form a two parameter family. In this paper we give a complete classification of the string-like solutions of this system. We show that the parameter plane is composed of two different regions with the following characteristics: One region contains the standard asymptotically conic cosmic string solutions together with a second kind of solutions with Melvin-like asymptotic behavior. The other region contains two types of solutions with bounded radial extension. The border between the two regions is the curve of maximal angular deficit of $2\pi$.