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Geodesic motions of test particles in a relativistic core–shell spacetime

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Abstract

In this paper, we discuss the geodesic motions of test particles in the intermediate vacuum between a monopolar core and an exterior shell of dipoles, quadrupoles and octopoles. The radii of the innermost stable circular orbits at the equatorial plane depend only on the quadrupoles. A given oblate quadrupolar leads to the existence of two innermost stable circular orbits, and their radii are larger than in the Schwarzschild spacetime. However, a given prolate quadrupolar corresponds to only one innermost stable circular orbit, and its radius is smaller than in the Schwarzschild spacetime. As to the general geodesic orbits, one of the recently developed extended phase space fourth order explicit symplectic-like methods is efficiently applicable to them although the Hamiltonian of the relativistic core–shell system is not separable. With the aid of both this fast integrator without secular growth in the energy errors and gauge invariant chaotic indicators, the effect of these shell multipoles on the geodesic dynamics of order and chaos is estimated numerically.

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Acknowledgements

The authors are very grateful to an anonymous referee for many useful suggestions. This research has been supported by the National Natural Science Foundation of China under Grant Nos. 11533004 and 11663005 and the Natural Science Foundation of Jiangxi Province under Grant No. 20153BCB22001.

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Authors and Affiliations

  1. Department of Physics and Institute of Astronomy, Nanchang University, Nanchang, 330031, China

    Lei Liu, Xin Wu & Guoqing Huang

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  1. Lei Liu
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  2. Xin Wu
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  3. Guoqing Huang
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Correspondence to Xin Wu.

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Liu, L., Wu, X. & Huang, G. Geodesic motions of test particles in a relativistic core–shell spacetime. Gen Relativ Gravit 49, 28 (2017). https://doi.org/10.1007/s10714-017-2193-z

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