Superintegrable models related to near horizon extremal Myers-Perry black hole in arbitrary dimension

TL;DR

This paper analyzes the integrability and superintegrability of spherical mechanics linked to near horizon extremal Myers-Perry black holes in arbitrary dimensions, revealing maximal superintegrability in odd dimensions and near-maximal in even dimensions.

Contribution

It systematically studies the integrability of these models, providing explicit analysis in action-angle variables and highlighting differences between odd and even dimensions.

Findings

Maximal superintegrability in odd dimensions

Near-maximal superintegrability in even dimensions

Explicit action-angle variable formulation

Abstract

We provide a systematic account of integrability of the spherical mechanics associated with the near horizon extremal Myers-Perry black hole in arbitrary dimension for the special case that all rotation parameters are equal. The integrability is established both in the original coordinates and in action-angle variables. It is demonstrated that the spherical mechanics associated with the black hole in d=2n+1 is maximally superintegrable, while its counterpart related to the black hole in d=2n lacks for only one integral of motion to be maximally superintegrable.