Simulations of gravitational collapse in null coordinates: II. Critical collapse of an axisymmetric scalar field

TL;DR

This paper presents the first null-coordinate simulations of axisymmetric scalar field collapse, showing the persistence of spherical critical behavior under moderate non-sphericity and analyzing the evolution of non-spherical perturbations.

Contribution

It demonstrates that the spherical Choptuik solution remains valid for moderately non-spherical initial data in null-coordinate simulations, extending understanding of critical collapse.

Findings

Spherical critical solution persists with moderate non-sphericity.

Non-sphericity evolves as an almost-linear perturbation.

Final collapse is dominated by non-spherical effects.

Abstract

We present the first numerical simulations in null coordinates of the collapse of nonspherical regular initial data to a black hole. We restrict to twist-free axisymmetry, and re-investigate the critical collapse of a non-spherical massless scalar field. We find that the Choptuik solution governing scalar field critical collapse in spherical symmetry persists when fine-tuning moderately non-spherical initial data to the threshold of black hole formation. The non-sphericity evolves as an almost-linear perturbation until the end of the self-similar phase, and becomes dominant only in the final collapse to a black hole. We compare with numerical results of Choptuik et al, Baumgarte, and Marouda et al, and conclude that they have been able to evolve somewhat more non-spherical solutions. Future work with larger deviations from spherical symmetry, and in particular vacuum collapse, will require a different choice of radial coordinate that allows the null generators to reconverge locally.