Polar magnetic fields in black-hole space-times

TL;DR

This paper models magnetic fields around black holes by solving Maxwell's equations in Schwarzschild and Kerr spacetimes, analyzing charged particle orbits and their stability in these complex electromagnetic environments.

Contribution

It provides explicit solutions for axially symmetric magnetic and electric fields near black holes, including the effects of rotation and multipole field combinations.

Findings

Circular equatorial orbits exist in odd-multipole magnetic fields.

Stable orbits can occur at specific radii in combined multipole fields.

Field configurations can cause radial variations in magnetic orientation and particle motion.

Abstract

To model magnetic fields of compact objects we solve the Maxwell equations in the background of the exterior static Schwarzschild and slowly rotating Kerr space-times. We impose the boundary condition that the electromagnetic fields are to vanish at infinity. A full set of solutions is obtained, describing axially symmetric magnetic fields, supplemented by axial electric fields in the case of non-vanishing rotation of the gravitational background. We study the motion of charged test particles in these combined gravitational and electromagnetic fields, in particular considering the conditions for circular equatorial orbits. Such 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.