Construction of Explicit Symplectic Integrators in General Relativity. II. Reissner–Nordström Black Holes

Abstract

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 construction of explicit symplectic integrators for a Hamiltonian of charged particles moving around a Reissner–Nordström 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 desirable properties in their long-term stability, precision, and efficiency for appropriate choices of step size. For the applicability of one of the new algorithms, the effects of 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 becomes strong with an increase of the magnetic parameter from a global phase-space structure. No variation of the black hole’s charge other than the Coulomb part affects the regular and chaotic dynamics of the particles’ orbits. A positive Coulomb part more easily induces chaos than a negative one.