Classification of Static, Spherically Symmetric Solutions of the Einstein-Yang-Mills Theory with Positive Cosmological Constant

TL;DR

This paper provides a comprehensive classification of all static, spherically symmetric solutions in SU(2) Einstein-Yang-Mills theory with a positive cosmological constant, including their maximal extensions and causal structures.

Contribution

It offers a complete classification framework for these solutions, extending radial solutions to their maximal intervals and analyzing their global causal structures.

Findings

Complete classification of solutions with regular origins.

Construction of Carter-Penrose diagrams for all solutions.

Phase space analysis of solution behaviors.

Abstract

We give a complete classification of all static, spherically symmetric solutions of the SU(2) Einstein-Yang-Mills theory with a positive cosmological constant. Our classification proceeds in two steps. We first extend solutions of the radial field equations to their maximal interval of existence. In a second step we determine the Carter-Penrose diagrams of all 4-dimensional space-times constructible from such radial pieces. Based on numerical studies we sketch a complete phase space picture of all solutions with a regular origin.