Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes

TL;DR

This paper demonstrates that all higher-dimensional Kerr-NUT-AdS spacetimes possess a universal Killing-Yano tensor, revealing hidden symmetries and extending known 4D results to higher dimensions.

Contribution

It proves the existence of a universal Killing-Yano tensor in all higher-dimensional Kerr-NUT-AdS solutions, generalizing the 4D hidden symmetry to higher dimensions.

Findings

Existence of a universal Killing-Yano tensor in higher dimensions

Explicit construction of Killing-Yano and Killing tensors

Discussion of properties of these tensors in higher-dimensional spacetimes

Abstract

It is well known that 4-dimensional Kerr-NUT-AdS spacetime possesses the hidden symmetry associated with the Killing-Yano tensor. This tensor is "universal" in the sense that there exist coordinates where it does not depend on any of the free parameters of the metric. Recently the general higher dimensional Kerr-NUT-AdS solutions of the Einstein equations were obtained. We demonstrate that all these metrics with arbitrary rotation and NUT parameters admit a universal Killing-Yano tensor. We give an explicit presentation of the Killing-Yano and Killing tensors and briefly discuss their properties.