The spinning bodies motion stability by lyapunov in an axially symmetric gravitational field

Ryabushko, A.P.; Bakhan'kov, A. A.

doi:10.1007/bf00767275

Cited by 3 publications

(2 citation statements)

References 4 publications

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“…In fact as it has been argued in [33] the deviation vectors may be used to define Lyapunov indices in general relativity for either geodesic or non-geodesics flows. The method of Lyapunov indices has been applied to study the stability of circular or non-circular orbits of spinning particles in [9,10,11,15]. In particular in [11] it was shown that using different supplementary conditions may result in different stability behaviour of spinning particles orbiting the Schwarzchild black hole.…”

Section: Introductionmentioning

confidence: 99%

“…Following the ideas presented in the latter reference, solutions describing circular or nearly circular orbits in various black hole space-times have been found. Different aspects of such orbits have been studied in the case of Lense-Thirring space-time in [9], in the case of Schwarzschild space-time in [10,11,12,13,14] (also in [15] for non-circular orbits), in the case of Kerr black hole in [16,17,18,19,20,21,22,23,24], in the case of Reissner-Nordström black hole in [25], and in the case of Weyl space-time in [26]. An alternative framework has been used in [27,28] and [29] to study orbits of spinning particles in Schwarzschild and Kerr-Newman space-times respectively.…”

Section: Introductionmentioning

confidence: 99%

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Stability of circular orbits of spinning particles in Schwarzschild-like space–times

Mohseni

2010

Gen Relativ Gravit

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Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits are stable against radial perturbations. The general criterion for stability against normal perturbations is obtained. Explicit calculations are performed in the case of the Schwarzschild space-time leading to the conclusion that the orbits are stable.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability of circular orbits of spinning particles in Schwarzschild-like space–times

Mohseni

2010

Gen Relativ Gravit

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Stability of noncircular and infinite motions of test bodies in general relativity

Bakhan'kov¹,

Ryabushko²

1989

Gen Relat Gravit

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Spin-geodesic deviations in the Kerr spacetime

Bini

Geralico

2011

Phys. Rev. D

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The dynamics of extended spinning bodies in the Kerr spacetime is investigated in the pole-dipole particle approximation and under the assumption that the spin-curvature force only slightly deviates the particle from a geodesic path. The spin parameter is thus assumed to be very small and the back reaction on the spacetime geometry neglected. This approach naturally leads to solve the Mathisson-Papapetrou-Dixon equations linearized in the spin variables as well as in the deviation vector, with the same initial conditions as for geodesic motion. General deviations from generic geodesic motion are studied, generalizing previous results limited to the very special case of an equatorial circular geodesic as the reference path.Comment: 19 pages, 6 figures; published versio

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The spinning bodies motion stability by lyapunov in an axially symmetric gravitational field

Cited by 3 publications

References 4 publications

Stability of circular orbits of spinning particles in Schwarzschild-like space–times

Stability of circular orbits of spinning particles in Schwarzschild-like space–times

Stability of noncircular and infinite motions of test bodies in general relativity

Spin-geodesic deviations in the Kerr spacetime

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