Geometry, conformal Killing-Yano tensors and conserved “currents”


Authors: Ulf Lindström and Özgür Sar{\i}o\u{g}lu

Preprint number: UUITP-28/22

Abstract: In this brief letter we derive some useful identities relating conformal Killing-Yano tensors (CKYTs) and geometric quantities. We then use these identities to construct covariantly conserved “currents”.  We conclude that rank-$n$ currents linear in rank-$n$ CKYTs $k$ and second order in derivatives  must have a simple form in terms of $dk$. Using the Pleba\'nski-Demia\'nski and the Kerr-Newman metrics, we show how these currents can be used to define charges. By construction, these currents are covariant under a general conformal rescaling of the metric.