Spatially Compact Solutions and Stabilization in Einstein-Yang-Mills-Higgs Theories

TL;DR

This paper introduces new, stable, spatially compact solutions to Einstein-Yang-Mills-Higgs equations, revealing a stabilization phenomenon where certain unstable modes vanish as the parameter alpha varies.

Contribution

It presents novel static, spherically symmetric solutions with regular, compact spacetimes in Einstein-Yang-Mills-Higgs theories, including a class with nodeless, stable Yang-Mills amplitude.

Findings

Nodeless solutions are linearly stable.

Unstable modes of solutions with nodes disappear as alpha varies.

Solutions form continuous families parametrized by alpha.

Abstract

New solutions to the static, spherically symmetric Einstein-Yang-Mills-Higgs equations with the Higgs field in the triplet resp. doublet representation are presented. They form continuous families parametrized by $\alpha=M_W/M_Pl$ ($M_W$ resp. $M_Pl$ denoting the W-boson resp. the Planck mass). The corresponding spacetimes are regular and have spatially compact sections. A particularly interesting class with the Yang-Mills amplitude being nodeless is exhibited and is shown to be linearly stable with respect to spherically symmetric perturbations. For some solutions with nodes of the Yang-Mills amplitude a new stabilization phenomenon is found, according to which their unstable modes disappear as $\alpha$ increases (for the triplet) or decreases (for the doublet).