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arXiv · 1412.7033

Integrability of Particle System around a Ring Source as the Newtonian Limit of a Black Ring

Takahisa Igata·Hideki Ishihara·Hirotaka Yoshino
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Abstract

The geodesic equation in the five-dimensional singly rotating black ring is non-integrable unlike the case of the Myers-Perry black hole. In the Newtonian limit of the black ring, its geodesic equation agrees with the equation of motion of a particle in the Newtonian potential due to a homogeneous ring gravitational source. In this paper, we show that the Newtonian equation of motion allows the separation of variables in the spheroidal coordinates, providing an non-trivial constant of motion quadratic in momenta. This shows that the Newtonian limit of a black ring recovers the symmetry of its geodesic system, and the geodesic chaos is caused by relativistic effects.

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Takahisa Igata, Hideki Ishihara, Hirotaka Yoshino. 2014-12-22. Integrability of Particle System around a Ring Source as the Newtonian Limit of a Black Ring. https://doi.org/10.1103/physrevd.91.084042

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