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arXiv · 2006.05052

Chaotic particle motion around a homogeneous circular ring

Takahisa Igata
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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.

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Takahisa Igata. 2020-06-09. Chaotic particle motion around a homogeneous circular ring. https://doi.org/10.1103/physrevd.102.044019

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