Einstein-Yang-Mills Solitons: The Role of Gravity

TL;DR

This paper investigates how gravity influences Einstein-Yang-Mills solitons, deriving an analytic lower bound on their mass-to-radius ratio and confirming it with numerical results.

Contribution

It provides an analytical lower bound on the mass-to-radius ratio necessary for Einstein-Yang-Mills solitons, clarifying gravity's balancing role.

Findings

Derived a lower bound of 2/3 for the mass-to-radius ratio.

Analytical results agree with numerical calculations.

Identified gravity's critical role in soliton stability.

Abstract

The canonical Bartnik-McKinnon solitons are regular solutions of the coupled Einstein-Yang-Mills system in which gravity may balance the repulsive nature of the Yang-Mills field. We examine the role played by gravity in balancing the system and determine its strength. In particular, we obtain an analytic lower bound on the fundamental mass-to-radius ratio, max{2m(r)/r}>2/3, which is a necessary condition for the existence of globally regular Einstein-Yang-Mills solitons. Our analytical results are in accord with numerical calculations.