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    Recurrence plots and chaotic motion around Kerr black hole

    Zdeněk Stuchlík · 01 října, 2010 · Fyzika · 0 comments
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    Publication date: Oct 2010

    Abstract:
    We study the motion of charged test particles around a Kerr black hole
    immersed in the asymptotically uniform magnetic field, concluding that
    off-equatorial stable orbits are allowed in this system. Being
    interested in dynamical properties of these astrophysically relevant
    orbits we employ rather novel approach based on the analysis of
    recurrences of the system to the vicinity of its previous states. We use
    recurrence plots (RPs) as a tool to visualize recurrences of the
    trajectory in the phase space. Construction of RPs is simple and
    straightforward regardless of the dimension of the phase space, which is
    a major advantage of this approach when compared to the „traditional“
    methods of the numerical analysis of dynamical systems (for instance the
    visual survey of Poincaré surfaces of section, evaluation of the
    Lyapunov spectra etc.). We show that RPs and their quantitative measures
    (obtained from recurrence quantification analysis-RQA) are powerful
    tools to detect dynamical regime of motion (regular vs. chaotic) and
    precisely locate the transitions between these regimes.

    Authors:
    Kopáček, Ondřej; Kovář, Jiří; Karas, Vladimír; Stuchlík, Zdeněk;

    http://adsabs.harvard.edu/abs/2010AIPC.1283..278K

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