Self-similar spherically symmetric wave maps coupled to gravity

We investigate spherically symmetric continuously self-similar (CSS) solutions in the $\mathrm{SU}\left(2\right)\mathrm{}$ sigma model coupled to gravity. Using mixed numerical and analytical methods, we provide evidence for the existence (for small coupling) of a countable family of regular CSS solutions. This fact is argued to have important implications for the ongoing studies of black hole formation in the model.