Comment on "Obstructions to the Existence of Static Cosmic Strings in an Abelian Higgs Model"

TL;DR

This paper critiques recent claims about obstructions to static cosmic string solutions in the Einstein-Maxwell-Higgs system, highlighting inconsistencies with earlier results and introducing a new, stronger condition.

Contribution

It provides a critical analysis of recent obstructions, clarifies inconsistencies with prior work, and proposes a new, more restrictive condition for the existence of solutions.

Findings

Some obstructions are inconsistent with earlier results

A new, stronger condition for solution existence is proposed

Clarifies the relationship between recent and prior findings

Abstract

There has been considerable interest in the possible cosmic string configurations and Y. Yang has recently derived intriguing obstructions to the existence of cylindrically symmetric solutions in the Bogomol'nyi critical phase of the Einstein-Maxwell-Higgs system. In this comment, we would like to mention some earlier results and recent progress which were not reflected there but are important in connection with the obstructions he claimed. Some of his obstructions are not consistent with the ealier results. Also, we give a new condition stronger than those found before.