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Chaotic particle motion around a homogeneous circular ring

By Takahisa Igata

Abstract

We consider test particle motion in a gravitational field generated by a homogeneous circular ring placed in $n$-dimensional Euclidean space. We observe that there exist no stable stationary orbits in $n=6, 7, \ldots, 10$ but exist in $n=3, 4, 5$ and clarify the regions in which they appear. In $n=3$, we show that the separation of variables of the Hamilton-Jacobi equation does not occur though we find no signs of chaos for stable bound orbits. Since the system is integrable in $n=4$, no chaos appears. In $n=5$, we find some chaotic stable bound orbits. Therefore, this system is nonintegrable at least in $n=5$ and suggests that the timelike geodesic system in the corresponding black ring spacetimes is nonintegrable.Comment: 21 pages, 4 figures; v2: minor revision, add references; v3: published versio

Topics: General Relativity and Quantum Cosmology, Astrophysics - Earth and Planetary Astrophysics, High Energy Physics - Theory
Publisher: 'American Physical Society (APS)'
Year: 2020
DOI identifier: 10.1103/PhysRevD.102.044019
OAI identifier: oai:arXiv.org:2006.05052

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