Applicability of the 0-1 test for chaos in magnetized Kerr-Newman spacetimes

The dynamics of electrically neutral or charged particles around a magnetized Kerr-Newman black hole immersed in an external electromagnetic field can be described by a dimensionless Hamiltonian system. This Hamiltonian is given an appropriate time transformation, which allows for construction of explicit symplectic integrators. Selecting one of the integrators with good accuracy, long-term stabilized Hamiltonian error behavior and less computational cost, we employ the 0-1 binary test correlation method to distinguish between regular and chaotic dynamics of electrically neutral or charged particles. The correlation method is almost the same as the techniques of Poincare map and fast Lyapunov indicators in identifying the regular and chaotic two cases. It can well describe the dependence of the transition from regularity to chaos on varying one or two dynamical parameters. From a statistical viewpoint, chaos occurs easily under some circumstances with an increase of the external magnetic field strength and the particle electric charge and energy or a decrease of the black hole spin and the particle angular momentum. A small change of the black hole electric charge does not very sensitively affect the dynamics of neutral particles. With the black hole electric charge increasing, positively charged particles do not easily yield chaotic motions, but negatively charged particles do. On the other hand, the effect of a small change of the black hole magnetic charge on the dynamical transition from order to chaos has no universal rule.