Spherically symmetric Yang-Mills solutions in a 5-dimensional (Anti-) de Sitter space-time

TL;DR

This paper investigates five-dimensional Einstein-Yang-Mills solutions with a cosmological constant, deriving effective four-dimensional models, and analyzes spherically symmetric solutions both analytically and numerically, revealing bifurcations with known (Anti-) de Sitter-Reissner-Nordstrom solutions.

Contribution

It introduces a dimensional reduction approach to analyze spherically symmetric solutions in a 5D Einstein-Yang-Mills framework with a cosmological constant, including analytical and numerical results.

Findings

Analytical solutions in specific limits

Numerical solutions for vanishing dilaton coupling

Bifurcation with (Anti-) de Sitter-Reissner-Nordstrom solutions

Abstract

We consider an Einstein-Yang-Mills Lagrangian in a five dimensional space-time including a cosmological constant. Assuming all fields to be independent of the extra coordinate, a dimensional reduction leads to an effective (3+1)-dimensional Einstein-Yang-Mills-Higgs-dilaton model where the cosmological constant induces a Liouville potential in the dilaton field. We construct spherically symmetric solutions analytically in specific limits and study the generic solutions for vanishing dilaton coupling numerically. We find that in this latter case the solutions bifurcate with the branch of (Anti-) de Sitter-Reissner-Nordstrom ((A)dSRN) solutions.