Hidden Symmetries and Black Holes

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 key equations, advancing understanding of black hole geometry.

Contribution

It highlights the role of a principal CKY tensor in generating hidden symmetries that enable complete integrability and separability in complex black hole spacetimes.

Findings

Existence of a principal CKY tensor leads to a hierarchy of Killing-Yano and Killing tensors.

Hidden symmetries ensure integrability of geodesic equations.

Equations of motion and perturbations are separable in Kerr-NUT-(A)dS metrics.

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 conformal Killing-Yano 2-form) allows one to generate a `tower' of Killing-Yano and Killing tensors responsible for hidden symmetries. These symmetries imply complete integrability of geodesic equations and the complete separation of variables in the Hamilton-Jacobi, Klein-Gordon, Dirac and gravitational perturbation equations in the general Kerr-NUT-(A)dS metrics. Equations of the parallel transport of frames along geodesics in these spacetimes are also integrable.