Hidden symmetries of black holes in five-dimensional supergravity

TL;DR

This paper uncovers hidden symmetries in five-dimensional supergravity black holes by demonstrating the existence of Killing-Yano forms with torsion, which explain separability properties and extend to gauged supergravity solutions.

Contribution

It reveals the presence of Killing-Yano 3-forms with torsion in five-dimensional supergravity black holes and connects these to known symmetries and separability properties.

Findings

Existence of Killing-Yano 3-form with torsion in 6D lift

Relation to Killing tensors and separability of Dirac equations

Extension to gauged supergravity solutions with specific gauge field conditions

Abstract

We consider a general charged, rotating black hole in five-dimensional STU supergravity, and show that its six-dimensional Kaluza-Klein lift admits a Killing-Yano 3-form with torsion. This underlies its known Killing tensors in five dimensions, and is related to the separability of torsion-modified Dirac equations. In the generalization to gauged supergravity, we present a five-dimensional Killing-Yano 3-form with torsion when two of the gauge fields are equal, and a Killing-Stackel tensor in the general 3-charge Wu solution.