Inducing Chaos by Breaking Axial Symmetry in a Black Hole Magnetosphere

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 (electrovacuum) 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.

Determination of chaotic behaviour in time series generated by charged particle motion around magnetized Schwarzschild black holes

“…The exact shape and structure of the magnetic fields around compact objects is still under examination, but the uniform magnetic field assumption introduced by Wald [12] can be used as first simple approximation to more complex fields. The charged test particle motion in such an asymptotically uniform configuration has been already studied in a large variety of papers that give significant insight into the astrophysical processes in vicinity of magnetized black holes [8,9,[13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In the present paper, we examine chaotic charged test particle dynamics around a Schwarzschild black hole immersed in an external uniform magnetic field, resulting under special initial condition of ionized Keplerian accretion disk.…”

Radiation Reaction of Charged Particles Orbiting a Magnetized Schwarzschild Black Hole

“…Below we test these equations in particular case of the motion of charged particles around Schwarzschild black hole immersed into external asymptotically uniform magnetic field. The motion of charged particles in the vicinity of magnetized Schwarzschild black hole is generally chaotic Kopáček & Karas (2014); Kopáček et al (2010). However, close to the minimum of the effective potential, which corresponds to the stable circular orbit, the motion of the charged particle is regular, being of harmonic character.…”

Quasi-harmonic oscillatory motion of charged particles around a Schwarzschild black hole immersed in a uniform magnetic field

“…Generally, the motion of a charged particle around a Schwarzschild black hole immersed in an external uniform magnetic field (Wald solution) is chaotic [36,42]. However, trajectories of charged particles, which are close to the minima of the effective potential corresponding to the stable circular orbits, still have a regular (harmonic) character [36].…”