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Integrability of particle system around a ring source as the Newtonian limit of a black ring

2014/12/22 by Takahisa Igata, Hideki Ishihara, Hirotaka Yoshino
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Cosmology and Gravitation Theories #Equations of motion #Geodesic #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Motion (physics) #Newtonian fluid #Newtonian limit #Physics #Ring (chemistry) #Solving the geodesic equations #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.91.084042

published as Phys. Rev. D 91, 084042 (2015) · 12 pages, 2 figures

arxiv created 2014/12/22 · openalex publication_date 2015/04/20 · arxiv updated 2015/04/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The geodesic equation in the five-dimensional singly rotating black ring is nonintegrable, 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 a nontrivial 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.

Citations