On the spherically symmetric Einstein-Yang-Mills-Higgs equations in Bondi coordinates

TL;DR

This paper extends previous results on global solutions for Einstein-Yang-Mills-Higgs equations in Bondi coordinates, improving assumptions on the potential and explaining differences in decay rates due to local charge effects.

Contribution

It generalizes earlier work to include the Einstein-Yang-Mills-Higgs system, with improved potential assumptions and an explanation for decay rate differences related to local charge.

Findings

Improved assumptions on the self-interaction potential.

Explanation of slower decay rates due to non-vanishing local charge.

Extension of global solution results to Einstein-Yang-Mills-Higgs system.

Abstract

We revisit and generalize, to the Einstein-Yang-Mills-Higgs system, previous results of D. Christodoulou and D. Chae concerning global solutions for the Einstein-scalar field and the Einstein-Maxwell-Higgs equations. The novelty of the present work is twofold. For one thing the assumption on the self-interaction potential is improved. For another thing explanation is furnished why the solutions obtained here and those proved by Chae for the Einstein-Maxwell-Higgs decay more slowly than those established by Christodoulou in the case of self-gravitating scalar fields. Actually this latter phenomenon stems from the non-vanishing local charge in Einstein-Maxwell-Higgs and Einstein-Yang-Mills-Higgs models.