Chaos in selfgravitating manybody systems: Lyapunov time dependence of $N$ and the influence of general relativity
Abstract
In selfgravitating $N$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 $N \sim 30$, 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 selfgravitating 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 EinsteinInfeldHoffmann 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 followup studies on the microscopic effect of general relativity on orbital chaos, and on the influence of higherorder crossterms in the Taylorseries expansion of the EinsteinInfeldHoffmann equations of motion.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.11012
 Bibcode:
 2021arXiv210911012P
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  High Energy Astrophysical Phenomena;
 General Relativity and Quantum Cosmology;
 Physics  Computational Physics
 EPrint:
 A&