Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries
arXiv:2011.12533 · doi:10.1093/mnras/staa3733
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, , 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 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 seem to be the most chaotic for the two cases of primary mass-ratios () 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 .
arXiv comment19 pages, 11 figures; Accepted for publication in MNRAS
References in corpus (61)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- Discovery of a binary AGN in the ultraluminous infrared galaxy NGC 6240 using Chandra
- Low-frequency gravitational-wave science with eLISA/NGO
- Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms
- Geometrical properties of local dynamics in Hamiltonian systems: the Generalized Alignment Index (GALI) method
- Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries
- Gravity Waves, Chaos, and Spinning Compact Binaries
- Lyapunov indices with two nearby trajectories in a curved spacetime
- The Origin of Double-Peaked Narrow Lines in Active Galactic Nuclei I: Very Large Array Detections of Dual AGNs and AGN Outflows
- Off-equatorial orbits in strong gravitational fields near compact objects -- II: halo motion around magnetic compact stars and magnetized black holes
- Description of Pseudo-Newtonian Potential for the Relativistic Accretion Disk around Kerr Black Holes
- Computation of Lyapunov Exponents in General Relativity
- Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals
- Chaotic motion of Charged Particles in an Electromagnetic Field Surrounding a Rotating Black Hole
- Off-equatorial orbits in strong gravitational fields near compact objects
- Corrections and Comments on the Multipole Moments of Axisymmetric Electrovacuum Spacetimes
- Free motion around black holes with discs or rings: between integrability and chaos - II
- Resurvey of order and chaos in spinning compact binaries
- The dynamics of precessing binary black holes using the post-Newtonian approximation
- 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"
- Stability Regions of Equilibrium Points in Restricted Four-Body Problem with Oblateness Effects
- Inducing chaos by breaking axial symmetry in a black hole magnetosphere
- Revealing the basins of convergence in the planar equilateral restricted four-body problem
- Ruling Out Chaos in Compact Binary Systems
- Exact General Relativistic Perfect Fluid Disks with Halos
- Free motion around black holes with discs or rings: between integrability and chaos - III
- Free motion around black holes with discs or rings: between integrability and chaos -- IV
- Diffusion and scaling in escapes from two-degree-of-freedom Hamiltonian systems
- Relativistic and Newtonian core-shell models: analytical and numerical results
- Comment on "Ruling out chaos in compact binary systems"
- The effect of Poynting-Robertson drag on the triangular Lagrangian points
- Chaos and Rotating Black Holes with Halos
- The deterministic nature of conservative post-Newtonian accurate dynamics of compact binaries with leading order spin-orbit interaction
- The Lagrange Equilibrium Points L_4 and L_5 in a Black Hole Binary System
- Pseudo-Newtonian planar circular restricted 3-body problem
- Second post-Newtonian Lagrangian dynamics of spinning compact binaries
- 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
- Fractal basins of escape and the formation of spiral arms in a galactic potential with a bar
- 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
- Escapes in Hamiltonian systems with multiple exit channels: Part I
- Chaos in Pseudo-Newtonian Black Holes with Halos
- Equilibrium points and basins of convergence in the linear restricted four-body problem with angular velocity
- Revealing the escape mechanism of three-dimensional orbits in a tidally limited star cluster
- On the conservation of the Jacobi integral in the post-Newtonian circular restricted three-body problem
- 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
- Fractal basin boundaries and escape dynamics in a multiwell potential
- The use of Kepler solver in numerical integrations of quasi-Keplerian orbits
- Stability of Orbits around a Spinning Body in a Pseudo-Newtonian Hill Problem
- Escapes in Hamiltonian systems with multiple exit channels: Part II
- A note on the equivalence of Lagrangian and Hamiltonian formulations at post-Newtonian approximations
- Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system
- Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system
- Revealing the Newton-Raphson basins of convergence in the circular pseudo-Newtonian Sitnikov problem
- Influence of the black hole spin on the chaotic particle dynamics within a dipolar halo
- Coalescence of Kerr Black Holes: Binary Systems from GW150914 to GW170814