On hidden symmetries of extremal Kerr-NUT-AdS-dS black holes

TL;DR

This paper explores the hidden symmetries of extremal Kerr-NUT-AdS-dS black holes, revealing how their near-horizon geometries inherit and modify these symmetries through explicit Killing-Yano potentials and tensor decompositions.

Contribution

It explicitly constructs the modified Killing-Yano potential for near-horizon geometries and shows the reducibility of the associated Killing tensor in terms of Killing vectors.

Findings

Near-horizon geometry admits four Killing vectors.

Hidden symmetry is carried over via a modified Killing-Yano potential.

Killing tensor is reducible to Casimir operators of Killing vectors.

Abstract

It is well known that the Kerr-NUT-AdS-dS black hole admits two linearly independent Killing vectors and possesses a hidden symmetry generated by a rank-2 Killing tensor. The near-horizon geometry of an extremal Kerr-NUT-AdS-dS black hole admits four linearly independent Killing vectors, and we show how the hidden symmetry of the black hole itself is carried over by means of a modified Killing-Yano potential which is given explicitly. We demonstrate that the corresponding Killing tensor of the near-horizon geometry is reducible as it can be expressed in terms of the Casimir operators formed by the four Killing vectors.