Generalized Killing-Yano equations in D=5 gauged supergravity
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.