Coordinate singularities of self-interacting vector field theories

TL;DR

This paper clarifies that certain singularities in self-interacting vector field theories are coordinate artifacts, not physical breakdowns, by analyzing criteria used to identify such singularities.

Contribution

The study demonstrates that the commonly used criterion based on the vector constraint equation indicates a coordinate singularity, which can be removed by a coordinate transformation, challenging previous interpretations.

Findings

Criterion (i) identifies coordinate singularities, not physical breakdowns.

Coordinate transformations can remove the identified singularities.

The physical validity of the theories remains unaffected by these coordinate singularities.

Abstract

Self-interacting vectors are seeing a burst of interest where various groups demonstrated that the field evolution ends in finite time. Two nonequivalent criteria have been offered to identify this breakdown: (i) the vector constraint equation cannot be satisfied beyond a point where the breakdown occurs, (ii) the dynamics is governed by an effective metric that becomes singular at the breakdown. We show that (i) identifies a coordinate singularity, and can be removed by a change of coordinates. Hence, it does not signify a physical problem, and cannot determine the validity of a theory.