Myers–Perry Conformal Mechanics

We investigate dynamics of probe particles moving in the near-horizon limit of an extremal Myers–Perry black hole with nonvanishing rotation parameters. We show, that in the case of non-equal non-vanishing rotational parameters the dynamics of probe particle can be described in unified way for both even and odd dimensions. In this way we extend to the even dimension the results on integrability and separability of variables in ellipsoidal coordinates in odd dimension presented in [1]. We find the general solution of the Hamilton–Jacobi equations for these systems and write down the explicit expressions for the Liouville integrals of motion.