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.
Chaos in Static Axisymmetric Spacetimes I : Vacuum Case
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abstract
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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gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Chaotic motion of particles around a Schwarzschild black hole in a swirling electromagnetic background
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.