Behavior of perturbations on spherically symmetric backgrounds in multi-Galileon theory

We consider multi-Galileon theory, the most general Galilean invariant theory with $N$ scalar fields linearly coupled to the trace of the stress-energy tensor. We study the behavior of perturbations on a static spherically symmetric background with a massive point source, and show that, under the assumptions of stability and successful Vainshtein screening, solutions cannot be found that are free of both superluminal propagation and slowly moving, strongly coupled fluctuations. The latter imply that the theoretical and phenomenological issues related to a very low strong-interaction scale cannot be avoided in this model.