Inducing chaos by breaking axial symmetry in a black hole magnetosphere

TL;DR

This paper investigates how breaking axial symmetry in a black hole magnetosphere, through magnetic field inclination, induces chaos in particle dynamics, with even slight misalignments leading to chaotic behavior.

Contribution

It introduces a model of a black hole magnetosphere with an inclined magnetic field, analyzing how non-axisymmetry triggers chaos in charged particle motion.

Findings

Small magnetic field inclinations induce chaos.

Breaking axial symmetry destroys conserved angular momentum.

Chaos increases with greater field misalignment.

Abstract

While the motion of particles near a rotating, electrically-neutral (Kerr), and charged (Kerr--Newman) black hole is always strictly regular, a perturbation in the gravitational or the electromagnetic field generally leads to chaos. The transition from regular to chaotic dynamics is relatively gradual if the system preserves axial symmetry, whereas non-axisymmetry induces chaos more efficiently. Here we study the development of chaos in an oblique (electro-vacuum) magnetosphere of a magnetized black hole. Besides the strong gravity of the massive source represented by the Kerr metric we consider the presence of a weak, ordered, large-scale magnetic field. An axially-symmetric model consisting of a rotating black hole embedded in an aligned magnetic field is generalized by allowing an oblique direction of the field having a general inclination, with respect to the rotation axis of the system. The inclination of the field acts as an additional perturbation to the motion of charged particles as it breaks the axial symmetry of the system and cancels the related integral of motion. The axial component of angular momentum is no longer conserved and the resulting system thus has three degrees of freedom. Our primary concern within this contribution is to find out how sensitive the system of bound particles is to the inclination of the field. We employ the method of the maximal Lyapunov exponent to distinguish between regular and chaotic orbits and to quantify their chaoticity. We find that even a small misalignment induces chaotic motion.