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

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–Nordström ((A)dSRN) solutions.