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Title: 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 (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 themore » 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.« less

Authors:
;  [1]
  1. Astronomical Institute, Academy of Sciences, Boční II, CZ-141 31 Prague (Czech Republic)
Publication Date:
OSTI Identifier:
22356790
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 787; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; ANGULAR MOMENTUM; AXIAL SYMMETRY; BLACK HOLES; CHAOS THEORY; CHARGED PARTICLES; DEGREES OF FREEDOM; DISTURBANCES; ELECTROMAGNETIC FIELDS; KERR METRIC; LYAPUNOV METHOD; MAGNETIC FIELDS; PERTURBATION THEORY

Citation Formats

Kopáček, O., and Karas, V., E-mail: kopacek@ig.cas.cz. Inducing chaos by breaking axial symmetry in a black hole magnetosphere. United States: N. p., 2014. Web. doi:10.1088/0004-637X/787/2/117.
Kopáček, O., & Karas, V., E-mail: kopacek@ig.cas.cz. Inducing chaos by breaking axial symmetry in a black hole magnetosphere. United States. doi:10.1088/0004-637X/787/2/117.
Kopáček, O., and Karas, V., E-mail: kopacek@ig.cas.cz. 2014. "Inducing chaos by breaking axial symmetry in a black hole magnetosphere". United States. doi:10.1088/0004-637X/787/2/117.
@article{osti_22356790,
title = {Inducing chaos by breaking axial symmetry in a black hole magnetosphere},
author = {Kopáček, O. and Karas, V., E-mail: kopacek@ig.cas.cz},
abstractNote = {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.},
doi = {10.1088/0004-637X/787/2/117},
journal = {Astrophysical Journal},
number = 2,
volume = 787,
place = {United States},
year = 2014,
month = 6
}
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