Critical-collapse behavior beyond spherical symmetry

Clarify the behavior of critical gravitational collapse in axisymmetry and beyond spherical symmetry, including whether the universality properties established for spherically symmetric massless-scalar collapse persist or are modified.

Background

The paper presents scalar-field critical collapse in spherical symmetry as a setting in which the threshold solution, critical exponent, and discrete self-similarity exhibit well-established universal behavior. It notes that extending this picture beyond spherical symmetry is complicated by fully nonlinear phenomena and by evidence that the vacuum critical exponent and echoing behavior are not universal across families of initial data. The authors therefore identify the behavior of critical collapse in axisymmetry and more general settings as unresolved.