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Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

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arxiv gr-qc/9505036 v3 pith:6SH3XAM7 submitted 1995-05-20 gr-qc astro-phchao-dynnlin.CD

Y.Sota , S.Suzuki , K.Maeda This is my paper · ORCID
classification gr-qcastro-phchao-dynnlin.CD
keywords spacetimesaxisymmetricchaoscriterionstaticfirstorbitsome
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We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.

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Cited by 6 Pith papers

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

  1. Geodesics and shadows of the spindle-deformed Kerr black hole

    gr-qc 2026-07 accept novelty 6.0 of 10

    In the spindle-deformed Kerr black hole, null geodesics separate at O(B²) while timelike do not; the deformation shifts the ISCO, can create an OSCO, and enlarges the shadow versus Kerr.

  2. Chaotic motion of particles around a Schwarzschild black hole in a swirling electromagnetic background

    gr-qc 2026-05 unverdicted novelty 5.0 of 10

    Numerical chaos indicators applied to the Schwarzschild-Bertotti-Robinson-Bonnor-Melvin family show that chaos occurs without swirling and that electromagnetic field strengths and directions tightly restrict bound orbits.

  3. Extreme-Mass-Ratio Inspirals Embedded in Dark Matter Halo: Existence of Homoclinic Orbit and Horizon-Induced Chaos

    gr-qc 2025-11 conditional novelty 5.0 of 10

    A Schwarzschild black hole embedded in a Dehnen dark-matter halo admits homoclinic orbits, and raising halo density, scale radius, or particle energy drives near-horizon motion from regular to chaotic while respecting...

  4. Probing phase transitions of regular black holes in anti-de Sitter space with Lyapunov exponent

    gr-qc 2025-10 conditional novelty 5.0 of 10

    For charged regular AdS black holes in quasi-topological gravity, the null-geodesic Lyapunov exponent jumps at the first-order phase transition and its phase difference vanishes at the critical point with exponent 1/2...

  5. Chaotic imprints of dark matter in extreme mass-ratio inspirals

    gr-qc 2026-02 reject novelty 4.0 of 10

    A toy model shows that adding a hand-made angle-dependent force to dark-matter spacetimes produces visual chaos and irregular numerical-Kludge waveforms, but the force is not a realistic dark-matter perturbation.

  6. Probing Thermodynamic Phase Transitions of 4D R-Charged Black Holes via Lyapunov Exponent

    gr-qc 2025-05 conditional novelty 4.0 of 10

    For 4D R-charged black holes, the Lyapunov exponent of unstable circular orbits tracks black hole phase transitions, and its discontinuity near the critical point shows a universal critical exponent of 1/2.

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