Continuous Self-Similarity Breaking in Critical Collapse

Abstract

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 critical 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 echoing period $Δ= \sqrt{2}π= 4.44$, reproducing the symmetries of the critical Choptuik solution.