Construction of a Second-order Six-dimensional Hamiltonian-conserving Scheme

Abstract Research has analytically shown that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen, and Sironi provides a first-order accuracy to numerical solutions six-dimensional conservative Hamiltonian system. Because this, new second-order is proposed. Numerical simulations galactic model hosting BL Lacertae object magnetized rotating black hole background support these analytical results. The method with appropriate time steps used explore effects varying parameters on presence chaos in two physical models. Chaos easily occurs as mass nucleus, internal perturbation parameter, anisotropy potential elliptical galaxy increase. dynamics charged particles around Kerr spacetime chaotic for larger energies particles, smaller initial angular momenta stronger magnetic fields. properties are not necessarily weakened when black-hole spin increases. can be any problems, including globally hyperbolic spacetimes readily available (3 + 1) split coordinates.