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

## TL;DR

This paper studies the motion of particles near extremal Myers-Perry black holes, revealing integrability and explicit constants of motion in complex rotating black hole backgrounds.

## Contribution

It demonstrates the separability of the Hamilton-Jacobi equation in ellipsoidal coordinates for general rotation parameters, providing explicit integrals of motion.

## Key findings

- Separation of variables in N-dimensional ellipsoidal coordinates.
- Explicit solutions to Hamilton-Jacobi equation.
- Identification of Liouville constants of motion.

## 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.