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Paper   IPM / P / 15131
School of Physics
  Title:   On integrability of geodesics in near-horizon extremal geometries
1.  H. Demirchian
2.  A. Nersessian
3.  S. Sadeghian
4.  M.M. Sheikh-Jabbari
  Status:   Published
  Journal: Phys. Rev. D
  No.:  10
  Vol.:  97
  Year:  2018
  Pages:   104004
  Supported by:  IPM
We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed in []. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals, discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.

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