Separability of multi-charge black holes in supergravity

TL;DR

This paper demonstrates that certain five-dimensional rotating black holes in supergravity allow separable solutions to key equations, enabling the construction of conformal Killing tensors and advancing understanding of their geometric properties.

Contribution

It provides the first explicit construction of conformal Killing tensors for these black hole solutions, including a general formula and specific examples.

Findings

Separable solutions exist for massless equations in these black hole backgrounds.

Conformal Killing tensors are explicitly constructed for specific black hole solutions.

A general formula for the co-vector field in the conformal Killing tensor equation is derived.

Abstract

In this paper, we show that some five-dimensional rotating black hole solutions of both gauged and ungauged supergravity, with independent rotation parameters and three charges admit separable solutions to the massless Hamilton-Jacobi and Klein-Gordon equations. This allows us to write down a conformal Killing tensor for the spacetime. Conformal Killing tensors obey an equation involving a co-vector field. We find this co-vector field in three specific examples, and also give a general formula for it.