On Asymmetric Zeipel–Lidov–Kozai Cycles in Mean Motion Resonances

Efimov, Sergey; Сидоренко, В. В.

doi:10.1134/s0010952520040097

Cited by 1 publication

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“…In this section, we focus on the latter, in particular since there is a rich body of literature about the associated phenomena observed in hierarchical triples. We refer to this theory as von Zeipel- Lidov-Kozai cycles (von Zeipel 1910;Lidov 1962;Kozai 1962), and there is copious literature about the theory (Efimov & Sidorenko 2020;Hamers 2021), its deeper consequences (de Elía et al 2019), or the observational aspects (Stephan et al 2021). Here we adopt the von Zeipel-Lidov-Kozai effect of testing the three-body methods for Newtonian and relativistic dynamics.…”

Section: Appendix C: Relativistic Von Zeipel-lidov-kozai Effectmentioning

confidence: 99%

Chaos in self-gravitating many-body systems

Zwart

Boekholt²,

Por

et al. 2022

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In self-gravitating N-body systems, small perturbations introduced at the start, or infinitesimal errors that are produced by the numerical integrator or are due to limited precision in the computer, grow exponentially with time. For Newton’s gravity, we confirm earlier results that for relatively homogeneous systems, this rate of growth per crossing time increases with N up to N ∼ 30, but that for larger systems, the growth rate has a weaker scaling with N. For concentrated systems, however, the rate of exponential growth continues to scale with N. In relativistic self-gravitating systems, the rate of growth is almost independent of N. This effect, however, is only noticeable when the system’s mean velocity approaches the speed of light to within three orders of magnitude. The chaotic behavior of systems with more than a dozen bodies for the usually adopted approximation of only solving the pairwise interactions in the Einstein-Infeld-Hoffmann equation of motion is qualitatively different than when the interaction terms (or cross terms) are taken into account. This result provides a strong motivation for follow-up studies on the microscopic effect of general relativity on orbital chaos, and on the influence of higher-order cross-terms in the Taylor-series expansion of the Einstein-Infeld-Hoffmann equations of motion.

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