Critical Collapse of the Massless Scalar Field in Axisymmetry

TL;DR

This study numerically investigates the critical collapse of axisymmetric massless scalar fields, revealing an unstable non-spherical mode that challenges previous perturbative predictions and leads to bifurcation into distinct symmetric regions.

Contribution

It demonstrates the existence of a non-spherical unstable mode in axisymmetric scalar field collapse, contrasting with prior perturbative analyses.

Findings

Identification of a growing non-spherical mode during collapse

Observation of bifurcation into two symmetric regions

Contradiction with previous perturbative stability results

Abstract

We present results from a numerical study of critical gravitational collapse of axisymmetric distributions of massless scalar field energy. We find threshold behavior that can be described by the spherically symmetric critical solution with axisymmetric perturbations. However, we see indications of a growing, non-spherical mode about the spherically symmetric critical solution. The effect of this instability is that the small asymmetry present in what would otherwise be a spherically symmetric self-similar solution grows. This growth continues until a bifurcation occurs and two distinct regions form on the axis, each resembling the spherically symmetric self-similar solution. The existence of a non-spherical unstable mode is in conflict with previous perturbative results, and we therefore discuss whether such a mode exists in the continuum limit, or whether we are instead seeing a marginally stable mode that is rendered unstable by numerical approximation.