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Critical Collapse of the Massless Scalar Field in Axisymmetry

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arxiv gr-qc/0305003 v1 pith:534TOCU5 submitted 2003-05-01 gr-qc

M.W. Choptuik , E.W. Hirschmann , S.L. Liebling , F.Pretorius This is my paper · ORCID
classification gr-qc
keywords criticalmodesolutionsphericallysymmetricaxisymmetriccollapsefield
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We present results from a numerical study of critical gravitational collapse of axisymmetric distributions of massless scalar field energy. We find threshold behavior that can be described by the spherically symmetric critical solution with axisymmetric perturbations. However, we see indications of a growing, non-spherical mode about the spherically symmetric critical solution. The effect of this instability is that the small asymmetry present in what would otherwise be a spherically symmetric self-similar solution grows. This growth continues until a bifurcation occurs and two distinct regions form on the axis, each resembling the spherically symmetric self-similar solution. The existence of a non-spherical unstable mode is in conflict with previous perturbative results, and we therefore discuss whether such a mode exists in the continuum limit, or whether we are instead seeing a marginally stable mode that is rendered unstable by numerical approximation.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonlinear Dynamics near the Threshold of Gravitational Collapse

    gr-qc 2026-07 conditional novelty 7.0 of 10

    Perturbation theory around flat space fails before black hole formation once peak luminosity exceeds ~10^-2 L_Planck; near criticality the spectrum flattens to 1/ω, matching the prediction from discrete self-similarity.

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    Any pure-metric higher-derivative gravity EFT with derivative-independent characteristics has a weakly hyperbolic physical spin-2 block that gauge fixing and constraint addition cannot remove.

  4. Comparing twist-free axisymmetric gravitational waves near the black hole threshold

    gr-qc 2026-07 conditional novelty 5.0 of 10

    Independent codes (bamps, prague, sphGR) agree on near-threshold vacuum wave collapse, confirming family-dependent scaling and quasi-universal strong-field features.

  5. Critical collapse of vacuum spacetimes: Nakamura wave initial data

    gr-qc 2026-06 unverdicted novelty 5.0 of 10

    Simulations with Nakamura wave initial data confirm approximately discretely self-similar threshold solutions in vacuum gravitational wave collapse, but without exact self-similarity or a unique critical solution, con...

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