2018/02/23 by Hovhannes Demirchian, Armen Nersessian, Saeedeh Sadeghian +1
Physics and Astronomy · Mathematics · #hep-th #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.97.104004
published as Phys. Rev. D 97, 104004 (2018) · v2: minor typos fixed, references added
arxiv created 2018/02/23 · arxiv updated 2018/05/09
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 arXiv:1703.00713. 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.