Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries

TL;DR

This paper investigates the dynamics of a test particle in a three-body system with Kerr-like primaries, incorporating beyond-Newtonian effects to analyze stability and chaos as the system transitions from Newtonian to relativistic regimes.

Contribution

It introduces a beyond-Newtonian potential for Kerr-like primaries and studies the resulting orbital dynamics, stability, and chaos, extending classical three-body problem analysis.

Findings

Chaos increases with the beyond-Newtonian parameter $\\epsilon$.

Chaos levels are higher than in Newtonian and Schwarzschild cases for all non-zero $\epsilon$.

Intermediate $\epsilon$ values exhibit the most chaotic behavior.

Abstract

The dynamics of the planar circular restricted three-body problem with Kerr-like primaries in the context of a beyond-Newtonian approximation is studied. The beyond-Newtonian potential is developed by using the Fodor-Hoenselaers-Perj\'es procedure. An expansion in the Kerr potential is performed and terms up-to the first non-Newtonian contribution of both the mass and spin effects are included. With this potential, a model for a test particle of infinitesimal mass orbiting in the equatorial plane of the two primaries is examined. The introduction of a parameter, $\epsilon$, allows examination of the system as it transitions from the Newtonian to the beyond-Newtonian regime. The evolution and stability of the fixed points of the system as a function of the parameter $\epsilon$ is also studied. The dynamics of the particle is studied using the Poincar\'e map of section and the Maximal Lyapunov Exponent as indicators of chaos. Intermediate values of $\epsilon$ seem to be the most chaotic for the two cases of primary mass-ratios ($=0.001,0.5$) examined. The amount of chaos in the system remains higher than the Newtonian system as well as for the planar circular restricted three-body problem with Schwarzschild-like primaries for all non-zero values of $\epsilon$.