Continuous Self-Similarity Breaking in Critical Collapse

TL;DR

This paper analyzes how near-critical scalar field configurations evolve from continuous to discrete self-similarity, revealing a universal symmetry-breaking process in gravitational collapse.

Contribution

It demonstrates, through analytic perturbation methods, that generic perturbations break continuous self-similarity into discrete self-similarity with a universal echoing period.

Findings

Perturbations cause departure from the Roberts solution in a universal manner.

Continuous self-similarity is broken into discrete self-similarity with a specific echoing period.

The results reproduce the symmetries observed in the critical Choptuik solution.

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 $\Delta = \sqrt{2}\pi = 4.44$, reproducing the symmetries of the critical Choptuik solution.