Structure-preserving numerical simulations of test particle dynamics around slowly rotating neutron stars within Hartle-Thorne approach
arXiv:2310.04514 · doi:10.1103/PhysRevD.108.103006
Abstract
In this paper, we explore the chaotic signatures of the geodesic dynamics for particles moving in the slowly rotating Hartle-Thorne spacetime; an approximate solution of vacuum Einstein field equations describing the exterior of a massive, deformed, and slowly rotating compact object. We employ the numerical study to examine the geodesics of prolate and oblate deformations for generic orbits and find the plateaus of the rotation curve, which are associated with the existence of Birkhoff islands in the Poincare surface of the section, where the ratio of the radial and polar frequency of geodesics remains constant throughout the island. We investigate various phase space structures, including hyperbolic points and chaotic regions in the neighborhood of resonant islands. Moreover, chaotic behavior is observed to be governed by the stickiness phenomenon, where chaotic orbits remain attached to stable ones for an extended duration before eventually diverging and are attracted toward the surface of the neutron star. The precision of the numerical integration used to simulate the particle's trajectories plays a crucial role in the structures of the Poincare surface of the section. We present a comparison of several efficient structure-preserving numerical schemes of order four applied to the considered non-integrable dynamical system and we investigate which schemes possess the canonical property of the Hamiltonian flow. Among the class of non-symplectic integrators, we employ the explicit Runge-Kutta method and explicit general linear method with a standard projection technique to project the numerical solution onto the desired manifold. The projection scheme admits the integration without any drift from the desired manifold and is computationally cost-effective. We are concerned with two crucial aspects -- long-term behaviour and CPU time consumption.
arXiv comment21 pages, 12 figures
References in corpus (32)
- Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits
- How to observe a non-Kerr spacetime
- The distribution of kHz QPO frequencies in bright LMXBs
- An observable signature of a background deviating from Kerr
- A comprehensive comparison of relativistic particle integrators
- Particle Dynamics Near Kerr-MOG Black Hole
- Determination of chaotic behaviour in time series generated by charged particle motion around magnetized Schwarzschild black holes
- The non-integrability of the Zipoy-Voorhees metric
- Testing spacetime symmetry through gravitational waves from extreme-mass-ratio inspirals
- Construction of Explicit Symplectic Integrators in General Relativity. I. Schwarzschild Black Holes
- Construction of explicit symplectic integrators in general relativity. II. Reissner-Nordstrom black holes
- Charged particle dynamics in parabolic magnetosphere around Schwarzschild black hole
- Construction of explicit symplectic integrators in general relativity. IV. Kerr black holes
- Inducing chaos by breaking axial symmetry in a black hole magnetosphere
- Free motion around black holes with discs or rings: between integrability and chaos -- IV
- Slowly-rotating curved acoustic black holes: Quasinormal modes, Hawking-Unruh radiation and quasibound states
- A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. II. Neutron Stars
- Generalized, energy-conserving numerical simulations of particles in general relativity. I. Time-like and null geodesics
- Quasinormal Modes of a Black Hole with Quadrupole Moment
- The modification of photon trapping orbits as a diagnostic of non-Kerr spacetimes
- Gravitational field of compact objects in general relativity
- Generalized, energy-conserving numerical simulations of particles in general relativity. II. Test particles in electromagnetic fields and GRMHD
- A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems
- A Note on the Construction of Explicit Symplectic Integrators for Schwarzschild Spacetimes
- The exact dynamical Chern Simons metric for a spinning black hole possesses a fourth constant of motion: A Dynamical-Systems-Based Conjecture
- Gauss collocation methods for efficient structure preserving integration of post-Newtonian equations of motion
- Recurrence Analysis as a tool to study chaotic dynamics of extreme mass ratio inspiral in signal with noise
- Epicyclic oscillations in the Hartle-Thorne external geometry
- Chaotic photon orbits and shadows of a non-Kerr object described by the Hartle-Thorne spacetime
- Comparing the full time-dependent Bogoliubov--de-Gennes equations to their linear approximation: A numerical investigation
- Chaotic Behavior of Geodesics in Kerr-like Spacetime
- Exploiting the hidden symmetry of spinning black holes: conservation laws and numerical tests