Non-abelian black strings and cosmological constant

We study the classical solutions of the Einstein-Yang-Mills model is five dimensions in the presence of a cosmological constant $\Lambda$. Using a spherically symmetric ansatz and assuming that the fields do not depend on the extra dimension, we transform the equations into a set of differential equations that we solve numerically. We construct new types of regular (resp. black holes) solutions which, close to the origin (resp. the event horizon) resemble the 4-dimensional gravitating monopole (resp. non abelian black hole) and study their global properties. In particular, we show that the solutions available for $\Lambda > 0$ present an essential singularity