Cosmological Analogues of the Bartnik--McKinnon Solutions

TL;DR

This paper classifies static, spherically symmetric solutions to Einstein--Yang--Mills equations with a cosmological constant, revealing three distinct classes based on $b4$ and the number of nodes, including generalizations of known solitons and new horizon solutions.

Contribution

It provides a numerical classification of solutions with cosmological constant, identifying three classes and their properties, extending the understanding of Einstein--Yang--Mills configurations.

Findings

Solutions generalize Bartnik--McKinnon solitons with cosmological horizons.

Existence of topologically spherical solutions including Einstein Universe.

Identification of a discrete family of finite-size solutions with horizons.

Abstract

We present a numerical classification of the spherically symmetric, static solutions to the Einstein--Yang--Mills equations with cosmological constant $\Lambda$. We find three qualitatively different classes of configurations, where the solutions in each class are characterized by the value of $\Lambda$ and the number of nodes, $n$, of the Yang--Mills amplitude. For sufficiently small, positive values of the cosmological constant, $\Lambda < \Llow(n)$, the solutions generalize the Bartnik--McKinnon solitons, which are now surrounded by a cosmological horizon and approach the deSitter geometry in the asymptotic region. For a discrete set of values $\Lambda_{\rm reg}(n) > \Lambda_{\rm crit}(n)$, the solutions are topologically $3$--spheres, the ground state $(n=1)$ being the Einstein Universe. In the intermediate region, that is for $\Llow(n) < \Lambda < \Lhig(n)$, there exists a discrete family of global solutions with horizon and ``finite size''.