Polar magnetic fields in black-hole space-times

Abstract

We study the motion of charged test particles in the combined gravitational and axially symmetric electromagnetic fields of a static Schwarzschild and slowly rotating Kerr spacetimes, in particular considering the conditions for circular equatorial orbits. We present a series calculation of the electromagnetic fields under the boundary condition that they are to vanish at infinity, and verify these with the closed-form expressions obtained previously in literature. Such particle orbits always exist in odd-multipole magnetic fields, and they can exist for particular radii in a combination of two or more even-multipole magnetic fields. Combinations of several odd-multipole fields can give rise to radial variation in the field orientation and the direction of motion of charged particles. Deviations from circularity are described using a perturbative approach. This also allows to study the stability of the parent circular orbits.