Chaotic particle motion around a homogeneous circular ring

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 $n=6,7,\dots ,10$ 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.

21 pages, 4 figures; v2: minor revision, add references; v3: published version

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Cited by in corpus (3)

• Stable circular orbits in higher-dimensional multi-black hole spacetimes
• Stable circular orbits in caged black hole spacetimes
• Chaos in a generalized Euler's three-body problem