Special symmetries of the charged Kerr-AdS black hole of D=5 minimal gauged supergravity

TL;DR

This paper demonstrates the separability of key equations in the charged Kerr-AdS black hole of D=5 minimal gauged supergravity, revealing special symmetries and constructing associated Killing tensors, with implications for understanding black hole geometries.

Contribution

It proves the separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in this black hole background and constructs the corresponding Killing tensor, highlighting special symmetries.

Findings

Hamilton-Jacobi equation is separable for arbitrary rotation parameters.

Klein-Gordon equation is separable in this background.

Dirac equation has separable solutions when rotation parameters are equal.

Abstract

In this note we prove that the Hamilton-Jacobi equation in the background of the recently discovered charged Kerr-AdS black hole of D=5 minimal gauged supergravity is separable, for arbitrary values of the two rotation parameters. This allows us to write down an irreducible Killing tensor for the spacetime. As a result we also show that the Klein-Gordon equation in this background is separable. We also consider the Dirac equation in this background in the special case of equal rotation parameters and show it has separable solutions. Finally we discuss the near-horizon geometry of the supersymmetric limit of the black hole.