Near horizon extremal Myers-Perry black holes and integrability of associated conformal mechanics

Abstract

We investigate dynamics of probe particles moving in the near-horizon limit of (2N+1)-dimensional extremal Myers-Perry black hole with arbitrary rotation parameters. We observe that in the most general case with nonequal nonvanishing rotational parameters the system admits separation of variables in N-dimensional ellipsoidal coordinates. This allows us to find solution of the corresponding Hamilton-Jacobi equation and write down the explicit expressions of Liouville constants of motion.

9 pages, no figures, v2: Minor changes to match the published version

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• ${\mathbb{CP}}^N$-Rosochatius system, superintegrability, supersymmetry
• Note on constants of motion in conformal mechanics associated with near horizon extremal Myers-Perry black holes
• Super 0--brane action on the coset space of $D(2,1;\alpha )$ supergroup
• Bianchi type-V spinning particle on 2-sphere
• Hidden symmetries of near-horizon extremal Kerr-AdS-NUT geometries
• Comment on "Generalized near horizon extreme binary black hole geometry"
• Remark on near-horizon geometry of extreme regular black holes
• Superintegrable deformations of oscillator and Coulomb systems