A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems
arXiv:1207.3175 · doi:10.1103/PhysRevD.86.124013
Abstract
By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for long term numerical integrations of geodesic orbits in spacetime backgrounds, whose corresponding Hamiltonian system is non-integrable, and, in general, for any non-integrable Hamiltonian system whose kinetic part depends on the position variables. We show by numerical examples that the new integrator is faster and more accurate i) than the standard symplectic integration schemes with or without standard adaptive step size controllers and ii) than an adaptive step Runge-Kutta scheme.
12 pages, 8 figures, 3 tables
References in corpus (15)
- Bumpy Black Holes in Alternate Theories of Gravity
- Observable Properties of Orbits in Exact Bumpy Spacetimes
- Geodesic equation in Schwarzschild--(anti-)de Sitter space--times: Analytical solutions and applications
- Lyapunov indices with two nearby trajectories in a curved spacetime
- How to observe a non-Kerr spacetime
- Gravitational waves from Extreme Mass Ratio Inspirals in non-pure Kerr spacetimes
- Free motion around black holes with discs or rings: between integrability and chaos - II
- The non-integrability of the Zipoy-Voorhees metric
- Symplectic structure of post-Newtonian Hamiltonian for spinning compact binaries
- Free motion around black holes with discs or rings: between integrability and chaos - I
- Dynamics of Black Hole Pairs I: Periodic Tables
- Symplectic Integration of Post-Newtonian Equations of Motion with Spin
- Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness
- Constraint on the quadrupole moment of super-massive black hole candidates from the estimate of the mean radiative efficiency of AGN
- Periodic Orbits and Escapes in Dynamical Systems
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- Inducing chaos by breaking axial symmetry in a black hole magnetosphere
- Investigating spinning test particles: spin supplementary conditions and the Hamiltonian formalism
- A Note on the Construction of Explicit Symplectic Integrators for Schwarzschild Spacetimes
- Explicit symplectic methods in black hole spacetimes
- Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations
- Dynamics of charged particles moving around Kerr black hole with inductive charge and external magnetic field
- Charged particle motions near non-Schwarzschild black holes with external magnetic fields in modified theories of gravity
- Explicit symplectic integrators with adaptive time steps in curved spacetimes
- Impact of electric charges on chaos in magnetized spacetimes
- Chaotic dynamics of pulsating spheres orbiting black holes