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.

8 pages,20 figures

References in corpus (13)

• 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
• 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
• Determination of chaotic behaviour in time series generated by charged particle motion around magnetized Schwarzschild black holes
• 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
• A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems
• A novel energy-conserving scheme for eight-dimensional systems

Cited by in corpus (9)

• Construction of explicit symplectic integrators in general relativity. IV. Kerr black holes
• 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
• Dynamics of charged particles moving around Kerr black hole with inductive charge and external magnetic field
• Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations
• 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