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

TL;DR

This paper develops explicit symplectic integrators for charged particle dynamics around Reissner-Nordstrom black holes, demonstrating their stability, accuracy, and the influence of electromagnetic parameters on orbital chaos.

Contribution

It extends symplectic integrator construction to Reissner-Nordstrom black holes with magnetic fields, enabling efficient long-term simulations of charged particle orbits.

Findings

Integrators maintain stability and accuracy over long simulations.

Magnetic parameter increases orbital chaos.

Coulomb potential sign influences regular and chaotic dynamics.

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.