Chaos in Schwarzschild spacetime

The motion of a spinning particle

Shingo Suzuki, Keiichi Maeda

    Research output: Contribution to journalArticle

    111 Citations (Scopus)

    Abstract

    We study the motion of a spinning test particle in Schwarzschild spacetime, analyzing the Poincaré map and the Lyapunov exponent. We find chaotic behavior for a particle with spin higher than some critical value (e.g., S cr~0.635μiM for the total angular momentum J=4μM), where μ and M are the masses of a particle and of a black hole, respectively. The inverse of the Lyapunov exponent in the most chaotic case is about five orbital periods, which suggests that chaos of a spinning particle may become important in some relativistic astrophysical phenomena. The "effective potential" analysis enables us to classify the particle orbits into four types as follows. When the total angular momentum J is large, some orbits are bounded and the "effective potentialsare classified into two types: (B1) one saddle point (unstable circular orbit) and one minimal point (stable circular orbit) on the equatorial plane exist for small spin; and (B2) two saddle points bifurcate from the equatorial plane and one minimal point remains on the equatorial plane for large spin. When J is small, no bound orbits exist and the potentials are classified into another two types: (U1) no extremal point is found for small spin; and (U2) one saddle point appears on the equatorial plane, which is unstable in the direction perpendicular to the equatorial plane, for large spin. The types (B1) and (U1) are the same as those for a spinless particle, but the potentials (B2) and (U2) are new types caused by spin-orbit coupling. The chaotic behavior is found only in the type (B2) potential. The "heteroclinic orbit," which could cause chaos, is also observed in type (B2).

    Original languageEnglish
    Pages (from-to)4848-4859
    Number of pages12
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume55
    Issue number8
    Publication statusPublished - 1997 Apr 15

    Fingerprint

    metal spinning
    chaos
    Chaos
    Space-time
    Orbit
    Motion
    orbits
    saddle points
    Saddlepoint
    circular orbits
    Chaotic Behavior
    Angular Momentum
    Lyapunov Exponent
    angular momentum
    Unstable
    exponents
    Spin-orbit Coupling
    Extremal Point
    Heteroclinic Orbit
    Effective Potential

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Nuclear and High Energy Physics
    • Physics and Astronomy (miscellaneous)

    Cite this

    Chaos in Schwarzschild spacetime : The motion of a spinning particle. / Suzuki, Shingo; Maeda, Keiichi.

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 55, No. 8, 15.04.1997, p. 4848-4859.

    Research output: Contribution to journalArticle

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