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 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 ∆ = √ 2π = 4.44, reproducing the symmetries of the Choptuik solution. Thus the role of the Robert solution is clarified as close to the Choptuik one out of solutions with stronger symmetry. PACS numbers: 04.70.Bw, 05.70.Jk Typeset using REVTEX Email: [email protected] 1