Circular orbits and related quasi-harmonic oscillatory motion of charged particles around weakly magnetized rotating black holes

TL;DR

This paper analyzes the motion of charged particles around weakly magnetized rotating black holes, revealing new types of oscillatory motion and the influence of magnetic fields on stable orbits.

Contribution

It provides analytical solutions for circular orbits and frequencies, classifies orbit types based on Lorentz force orientation, and uncovers novel toroidal epicyclic motions.

Findings

Stable orbits can extend below photon sphere radii.

Existence of toroidal epicyclic motion with high radial and vertical frequencies.

Magnetic field effects significantly alter orbital frequencies and stability.

Abstract

We study motion of charged particles in the field of a rotating black hole immersed into an external asymptotically uniform magnetic field, focusing on the epicyclic quasi-circular 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 analyse 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 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, $\omega_\mir$, vertical, $\omega_\mit$, and orbital, $\omega_\mip$, frequencies, finding significant differences in comparison to the epicyclic geodesic circular motion. The most important new phenomenon is existence of toroidal charged particle epicyclic motion with $\omega_\mir \sim \omega_{\mit} >> \omega_{\mip}$ that could occur around retrograde circular orbits with outward oriented Lorentz force. We demonstrate that for the rapidly rotating black holes the role of the 'Wald induced charge' can be relevant.