Construction of explicit symplectic integrators in general relativity. III. Reissner-Nordstrom-(anti)-de Sitter black holes

We give a possible splitting method to a Hamiltonian for the description of charged particles moving around the Reissner-Nordstrom-(anti)-de Sitter black hole with an external magnetic field. This Hamiltonian can be separated into six analytical solvable pieces, whose solutions are explicit functions of proper time. In this case, second- and fourth-order explicit symplectic integrators are easily available. They exhibit excellent long-term behavior in maintaining the boundness of Hamiltonian errors regardless of ordered or chaotic orbits if appropriate step-sizes are chosen. Under some circumstances, an increase of positive cosmological constant gives rise to strengthening the extent of chaos from the global phase space; namely, chaos of charged particles occurs easily for the accelerated expansion of the universe. However, an increase of the magnitude of negative cosmological constant does not. The different contributions on chaos are because the cosmological constant acts as a repulsive force in the Reissner-Nordstrom-de Sitter black hole, but an attractive force in the Reissner-Nordstrom-anti-de Sitter black hole.