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The Choptuik spacetime as an eigenvalue problem

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arxiv gr-qc/9507054 v2 pith:FGNDJOA5 submitted 1995-07-27 gr-qc

Carsten Gundlach This is my paper · ORCID
classification gr-qc
keywords blackcriticaldeltaeigenvaluefindholeproblemspacetime
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By fine-tuning generic Cauchy data, critical phenomena have recently been discovered in the black hole/no black hole "phase transition" of various gravitating systems. For the spherisymmetric real scalar field system, we find the "critical" spacetime separating the two phases by demanding discrete scale-invariance, analyticity, and an additional reflection-type symmetry. The resulting nonlinear hyperbolic boundary value problem, with the rescaling factor Delta as the eigenvalue, is solved numerically by relaxation. We find Delta = 3.4439 +/- 0.0004.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 108 citations worldwide. 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.

  2. Critical spacetime crystals in continuous dimensions

    gr-qc 2026-02 unverdicted novelty 7.0 of 10

    Numerical construction of a one-parameter family of discretely self-similar critical spacetimes for massless scalar collapse in continuous D>3, giving echoing period Delta(D) and Choptuik exponent gamma(D) with a maxi...

  3. Unveiling horizons in quantum critical collapse

    gr-qc 2025-09 unverdicted novelty 7.0 of 10

    Semiclassical quantum corrections in critical collapse yield a finite mass gap and transition from classical Type II to quantum Type I behavior, providing a quantum enforcement of weak cosmic censorship.

  4. Angle of Null Energy Condition Lines in Critical Spacetimes

    gr-qc 2024-11 conditional novelty 7.0 of 10

    In Choptuik critical collapse, the null energy condition saturation lines meet at the center with a universal angle α=2 arccot(D−1), numerically α≈0.64 in four dimensions.

  5. Quantum fate of the Choptuik naked singularity

    gr-qc 2026-06 unverdicted novelty 6.0 of 10

    Quantum backreaction generates horizons that cloak the Choptuik naked singularity, reducing its predictability violation to the standard black hole evaporation problem.

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