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A small deformation controlled by four free parameters to the Schwarzschildmetric could be referred to a nonspinning black hole solution in alternativetheories of gravity. Because such a non-Schwarzschild metric can be changedinto a Kerr-like black hole metric via a complex coordinate transformation, therecently proposed time-transformed explicit symplectic integrators for the Kerrtype spacetimes are suitable for a Hamiltonian system describing the motion ofcharged particles around the non-Schwarzschild black hole surrounded with anexternal magnetic field. The obtained explicit symplectic methods are based ona time-transformed Hamiltonian split into seven parts, whose analyticalsolutions are explicit functions of new coordinate time. Numerical tests showthat such explicit symplectic integrators for intermediate time-steps performgood long-term performance in stabilizing Hamiltonian errors regardless ofregular or chaotic orbits. One of the explicit symplectic integrators with thetechniques of Poincar\'{e} sections and fast Lyapunov indicators is applied toinvestigate the effects of the parameters including the four free deformationparameters on the orbital dynamical behavior. From the global phase-spacestructure, chaotic properties are typically strengthened under somecircumstances as any one of the energy and the magnitudes of magnetic parameterand negative deformation parameters increases. However, they are weakened wheneach of the angular momentum and positive deformation parameters increases.

Charged particle motions near non-Schwarzschild black holes with external magnetic fields in modified theories of gravity