Generalized Killing-Yano equations in D=5 gauged supergravity

TL;DR

This paper introduces a generalized form of Killing-Yano equations in five-dimensional gauged supergravity, incorporating torsion from the dual Maxwell flux, which aids in understanding black hole symmetries and equation separability.

Contribution

It extends Killing-Yano theory to include torsion effects in D=5 gauged supergravity, linking to black hole solutions and separability of fundamental equations.

Findings

Generalized Killing-Yano tensors exist with torsion in D=5 supergravity.

These tensors generate towers of Killing tensors.

Application to black hole spacetime explains equation separability.

Abstract

We propose a generalization of the (conformal) Killing-Yano equations relevant to D=5 minimal gauged supergravity. The generalization stems from the fact that the dual of the Maxwell flux, the 3-form *F, couples naturally to particles in the background as a `torsion'. Killing-Yano tensors in the presence of torsion preserve most of the properties of the standard Killing-Yano tensors, exploited recently for the higher-dimensional rotating black holes of vacuum gravity with cosmological constant. In particular, the generalized closed conformal Killing-Yano 2-form gives rise to the tower of generalized closed conformal Killing-Yano tensors of increasing rank which in turn generate the tower of Killing tensors. An example of a generalized Killing-Yano tensor is found for the Chong-Cvetic-Lu-Pope black hole spacetime [hepth/0506029]. Such a tensor stands behind the separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in this background.