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  • “School of Physic”

     
    Paper   IPM / Physic / 15131
       School of Physics
      Title: On integrability of geodesics in near-horizon extremal geometries
      Author(s):
    1 . H. Demirchian
    2 . A. Nersessian
    3 . S. Sadeghian
    4 . M.M. Sheikh-Jabbari
      Status: Preprint
      Journal:
      Year: 2018
      Supported by: IPM
      Abstract:
    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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