Circular orbits and related quasiharmonic oscillatory motion of charged particles around weakly magnetized rotating black holes

We study the motion of charged particles in the field of a rotating black hole immersed into an external asymptotically uniform magnetic field, focusing on the epicyclic quasicircular orbits near the equatorial plane. Separating the circular orbits into four qualitatively different classes according to the sign of the canonical angular momentum of the motion and the orientation of the Lorentz force, we analyze the circular orbits using the so-called force formalism. We find the analytical solutions for the radial profiles of velocity, specific angular momentum, and specific energy of the circular orbits in dependence on the black-hole dimensionless spin and the magnetic field strength. The innermost stable circular orbits are determined for all four classes of the circular orbits. The stable circular orbits with an outward-oriented Lorentz force can extend to radii lower than the radius of the corresponding photon circular geodesic. We calculate the frequencies of the harmonic oscillatory motion of the charged particles in the radial and vertical directions related to the equatorial circular orbits and study the radial profiles of the radial, ₑ; vertical, _; and orbital, _, frequencies, finding significant differences in comparison to the epicyclic geodesic circular motion. The most important new phenomenon is the existence of toroidal charged particle epicyclic motion with ₑ__ that could occur around retrograde circular orbits with an outward-oriented Lorentz force. We demonstrate that for the rapidly rotating black holes the role of the ``Wald induced charge'' can be relevant.