Continuous self-similarity breaking in critical collapse

This paper studies near-critical evolution of the spherically symmetric scalar field configurations close to the continuously self-similar solution. Using analytic perturbative methods, it is shown that a generic growing perturbation departs from the Roberts solution in a universal way. We argue that in the course of its evolution, initial continuous self-similarity of the background is broken into discrete self-similarity with an echoing period Delta = root 2 pi = 4.44, reproducing the symmetries of the critical Choptuik solution.