Critical Collapse Beyond Spherical Symmetry: General Perturbations of the Roberts Solution

TL;DR

This paper investigates non-spherical perturbations of a critical gravitational collapse solution, finding no unstable modes, which suggests the solution's stability beyond spherical symmetry.

Contribution

It provides the first exact analysis showing the absence of growing non-spherical perturbation modes in the Roberts solution.

Findings

No growing non-spherical modes found

Roberts solution is stable against non-spherical perturbations

Enhances understanding of critical collapse stability

Abstract

This paper studies the non-spherical perturbations of the continuously self-similar critical solution of the gravitational collapse of a massless scalar field (the Roberts solution). The exact analysis of the perturbation equations reveals that there are no growing non-spherical perturbation modes.