Hidden Symmetries of Higher-Dimensional Black Hole Spacetimes

TL;DR

This paper reviews how hidden symmetries in higher-dimensional black hole spacetimes, generated by a principal CKY tensor, lead to integrability and separability of fundamental equations.

Contribution

It demonstrates that the existence of a principal CKY tensor generates a hierarchy of symmetries enabling complete integrability and separability in Kerr-NUT-(A)dS spacetimes.

Findings

Complete integrability of geodesic equations

Separability of Hamilton-Jacobi, Klein-Gordon, and Dirac equations

Existence of a hierarchy of Killing-Yano and Killing tensors

Abstract

The paper contains a brief review of recent results on hidden symmetries in higher dimensional black hole spacetimes. We show how the existence of a principal CKY tensor (that is a closed non-degenerate conformal Killing-Yano 2-form) allows one to generate a `tower' of Killing-Yano and Killing tensors responcible for hidden symmetries. These symmetries imply complete integrability of geodesic equations and the complete separation of variables in the Hamilton-Jacobi, Klein-Gordon and Dirac equations in the general Kerr-NUT-(A)dS metrics.