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 reinvestigate the critical collapse of a nonspherical massless scalar field. We find that the Choptuik solution governing scalar field critical collapse in spherical symmetry persists when fine-tuning moderately nonspherical initial data to the threshold of black hole formation. The nonsphericity 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 nonspherical 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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ORCID for Carsten Gundlach: orcid.org/0000-0001-9585-5375

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