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

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.

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• Unveiling horizons in quantum critical collapse
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• Conformal compactification and affine-null metric formulation of the Einstein equations
• Gravitational Collapse of an Inhomogeneous Fluid in Rastall Theory
• Hierarchical formulation of the self-gravitating, n-dimensional, charged scalar field in spherical symmetry in affine null formalism