Construction of explicit symplectic integrators in general relativity. II. Reissner-Nordstrom black holes

Abstract

In a previous paper, second- and fourth-order explicit symplectic integrators were designed for a Hamiltonian of the Schwarzschild black hole. Following this work, we continue to trace the possibility of the construction of explicit symplectic integrators for a Hamiltonian of charged particles moving around a Reissner-Nordstrom black hole with an external magnetic field. Such explicit symplectic methods are still available when the Hamiltonian is separated into five independently integrable parts with analytical solutions as explicit functions of proper time. Numerical tests show that the proposed algorithms share the desirable properties in their long-term stability, precision and efficiency for appropriate choices of step sizes. For the applicability of one of the new algorithms, the effects of the black hole's charge, the Coulomb part of the electromagnetic potential and the magnetic parameter on the dynamical behavior are surveyed. Under some circumstances, the extent of chaos gets strong with an increase of the magnetic parameter from a global phase-space structure. No the variation of the black hole's charge but the variation of the Coulomb part is considerably sensitive to affect the regular and chaotic dynamics of particles' orbits. A positive Coulomb part is easier to induce chaos than a negative one.

arXiv comment8 pages,20 figures

References in corpus (24)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• Acceleration of charged particles due to chaotic scattering in the combined black hole gravitational field and asymptotically uniform magnetic field
• Possible signature of magnetic fields related to quasi-periodic oscillation observed in microquasars
• Transition from Regular to Chaotic Circulation in Magnetized Coronae near Compact Objects
• Supermassive black holes as possible sources of ultra high energy cosmic rays
• Chaotic motion of Charged Particles in an Electromagnetic Field Surrounding a Rotating Black Hole
• Determination of chaotic behaviour in time series generated by charged particle motion around magnetized Schwarzschild black holes
• Explicit methods in extended phase space for inseparable Hamiltonian problems
• Construction of Explicit Symplectic Integrators in General Relativity. I. Schwarzschild Black Holes
• On post-Newtonian orbits and the Galactic-center stars
• Inducing chaos by breaking axial symmetry in a black hole magnetosphere
• Symplectic Integration of Post-Newtonian Equations of Motion with Spin
• Generalized, energy-conserving numerical simulations of particles in general relativity. I. Time-like and null geodesics
• Effect of Electromagnetic Interaction on Galactic Center Flare Components
• Generalized, energy-conserving numerical simulations of particles in general relativity. II. Test particles in electromagnetic fields and GRMHD
• The Midpoint Rule as a Variational--Symplectic Integrator. I. Hamiltonian Systems
• A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems
• Slimplectic Integrators: Variational Integrators for General Nonconservative Systems
• Constraints on mass, spin and magnetic field of microquasar H~1743-322 from observations of QPOs
• A novel energy-conserving scheme for eight-dimensional systems
• The use of Kepler solver in numerical integrations of quasi-Keplerian orbits

Cited by in corpus (31)

• Construction of explicit symplectic integrators in general relativity. IV. Kerr black holes
• Construction of explicit symplectic integrators in general relativity. III. Reissner-Nordstrom-(anti)-de Sitter black holes
• Structure-preserving numerical simulations of test particle dynamics around slowly rotating neutron stars within Hartle-Thorne approach
• Applying explicit symplectic integrator to study chaos of charged particles around magnetized Kerr black hole
• A Note on the Construction of Explicit Symplectic Integrators for Schwarzschild Spacetimes
• Explicit symplectic methods in black hole spacetimes
• Electromagnetic field and chaotic charged-particle motion around hairy black holes in Horndeski gravity
• 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
• Chaos in a Magnetized Modified Gravity Schwarzschild Spacetime
• Charged particle motions near non-Schwarzschild black holes with external magnetic fields in modified theories of gravity
• Equivalence between two charged black holes in dynamics of orbits outside the event horizons
• Energy-conserving integrator for conservative Hamiltonian systems with ten-dimensional phase space
• Semiexplicit Symplectic Integrators for Non-separable Hamiltonian Systems
• Explicit symplectic integrators with adaptive time steps in curved spacetimes
• Impact of electric charges on chaos in magnetized $Reissner-Nordstr\ddot{o}m$ spacetimes
• Preservation of Quadratic Invariants by Semiexplicit Symplectic Integrators for Non-separable Hamiltonian Systems
• Effects of coupling constants on chaos of charged particles in the $Einstein-\AE$ ther theory
• Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems
• Third type of spacetime with the coexistence of integrability and non-integrability
• Mutual Information for particle pair and its application to diagnose Chaos in Curved Spacetime
• The flow method for the Baker-Campbell-Hausdorff formula: exact results
• Study of chaos in rotating galaxies using extended force-gradient symplectic methods
• Measurement of the central Galactic black hole by extremely large mass-ratio inspirals
• Chaotic dynamics of charged particles near weakly magnetized black holes in Einstein-ModMax Theory
• Construction of second-order six-dimensional Hamiltonian-conserving scheme
• Explicit Symplectic Integrators for Massive Point Vortex Dynamics in Binary Mixture of Bose--Einstein Condensates
• The Influence of General Relativity on the Spins of Celestial Bodies in Inclined Orbits
• Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian
• Gravitational emissions and light curves of quasi-periodic orbits in Schwarzschild spacetime embedded in a Dehnen-type dark matter halo
• Discussion on the equivalence of two relativistic point-particle Lagrangians