We give a possible splitting method to a Hamiltonian for the description of charged particles moving around the Reissner–Nordstrm-(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 the 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 the negative cosmological constant does not. The different contributions to chaos are because the cosmological constant acts as a repulsive force in the Reissner–Nordstrm-de Sitter black hole, but an attractive force in the Reissner–Nordstrm-anti-de Sitter black hole.

我们为哈密顿量提供了一种可能的分裂方法，用于描述在外部磁场下围绕 Reissner-Nordstrm-(anti)-de Sitter 黑洞运动的带电粒子。这个哈密顿量可以分成六个解析可解部分，其解是适当时间的显式函数。在这种情况下，二阶和四阶显式辛积分器很容易获得。如果选择适当的步长，它们在保持哈密顿误差的边界方面表现出出色的长期行为，而不管是有序还是混沌轨道。在某些情况下，正宇宙常数的增加会导致来自全局相空间的混沌程度加强；即宇宙的加速膨胀容易产生带电粒子的混沌。然而，负宇宙学常数幅度的增加没有。对混沌的不同贡献是因为宇宙常数在 Reissner-Nordstrm-de Sitter 黑洞中充当排斥力，但在 Reissner-Nordstrm-anti-de Sitter 黑洞中充当吸引力。