Echoing and scaling in Einstein-Yang-Mills critical collapse

TL;DR

This paper confirms numerical findings of echoing and mass scaling in spherical Yang-Mills gravitational collapse by constructing the critical solution as an eigenvalue problem, revealing asymptotic self-similarity and precise critical parameters.

Contribution

It introduces a method to analyze the Yang-Mills critical solution as an eigenvalue problem, extending techniques for discrete self-similarity to non-scale-invariant fields.

Findings

Echoing period Delta = 0.73784 +/- 0.00002

Critical exponent gamma = 0.1964 +/- 0.0007

Asymptotic, not exact, self-similarity in the solution

Abstract

We confirm recent numerical results of echoing and mass scaling in the gravitational collapse of a spherical Yang-Mills field by constructing the critical solution and its perturbations as an eigenvalue problem. Because the field equations are not scale-invariant, the Yang-Mills critical solution is asymptotically, rather than exactly, self-similar, but the methods for dealing with discrete self-similarity developed for the real scalar field can be generalized. We find an echoing period Delta = 0.73784 +/- 0.00002 and critical exponent for the black hole mass gamma = 0.1964 +/- 0.0007.