Abstract
We mainly focus on the effects of small changes of parameters on the dynamics of charged particles around Kerr black holes surrounded by an external magnetic field, which can be considered as a tidal environment. The radial motions of charged particles on the equatorial plane are studied via an effective potential. It is found that the particle energies at the local maxima values of the effective potentials increase with an increase in the black hole spin and the particle angular momenta, but decrease with an increase of one of the inductive charge parameter and magnetic field parameter. The radii of stable circular orbits on the equatorial plane also increase, whereas those of the innermost stable circular orbits decrease. On the other hand, the effects of small variations of the parameters on the orbital regular and chaotic dynamics of charged particles on the non-equatorial plane are traced by means of a time-transformed explicit symplectic integrator, Poincaré sections and fast Lyapunov indicators. It is shown that the dynamics sensitivity depends on small variations in the inductive charge parameter, magnetic field parameter, energy, and angular momentum. Chaos occurs easily as each of the inductive charge parameter, magnetic field parameter, and energy increases but is weakened as the angular momentum increases. When the dragging effects of the spacetime increase, the chaotic properties are not always weakened under some circumstances.
Highlights
The Kerr metric that describes a rotating black hole is a solution to Einstein’s field equations of general relativity
The observed event-horizon-scale images of the supermassive black hole candidate in the center of the giant elliptical galaxy M87 are consistent with the dark shadow of a Kerr black hole predicted by general relativity [1]
The fourth invariable quantity related to the azimuthal motion of the particles is absent when the external electromagnetic fields are considered near the black hole
Summary
The Kerr metric that describes a rotating black hole is a solution to Einstein’s field equations of general relativity. The magnetic fields in the vicinity of the black holes destroy the integrability of these spacetimes in many problems, the radial motions of the charged particles on the equatorial plane are still integrable and solvable. It is mainly studied by means of an effective potential. The authors of [68] applied the time-transformed explicit symplectic integrators introduced in [67] to mainly explore the effect of the black hole spin on the chaotic motion of a charged particle around the Kerr black hole immersed in an external electromagnetic field.
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