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

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-Perjés 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 Poincaré 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 $\epsilon$.

19 pages, 11 figures; Accepted for publication in MNRAS

References in corpus (22)

• Lyapunov indices with two nearby trajectories in a curved spacetime
• Off-equatorial orbits in strong gravitational fields near compact objects -- II: halo motion around magnetic compact stars and magnetized black holes
• Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals
• Off-equatorial orbits in strong gravitational fields near compact objects
• Free motion around black holes with discs or rings: between integrability and chaos - II
• Resurvey of order and chaos in spinning compact binaries
• Symplectic structure of post-Newtonian Hamiltonian for spinning compact binaries
• Free motion around black holes with discs or rings: between integrability and chaos - I
• Revisit on "Ruling out chaos in compact binary systems"
• Inducing chaos by breaking axial symmetry in a black hole magnetosphere
• Revealing the basins of convergence in the planar equilateral restricted four-body problem
• The effect of Poynting-Robertson drag on the triangular Lagrangian points
• Chaos in two black holes with next-to-leading order spin-spin interactions
• Collinear solution to the general relativistic three-body problem
• Newtonian and Pseudo-Newtonian Hill Problem
• Basins of convergence of equilibrium points in the pseudo-Newtonian planar circular restricted three-body problem
• A Hamiltonian system of three degrees of freedom with eight channels of escape: The Great Escape
• Equilibrium points and basins of convergence in the linear restricted four-body problem with angular velocity
• Periodic Orbits and Escapes in Dynamical Systems
• GRB 090510: a genuine short-GRB from a binary neutron star coalescing into a Kerr-Newman black hole
• Stability of Orbits around a Spinning Body in a Pseudo-Newtonian Hill Problem
• Revealing the Newton-Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem