Geometry, conformal Killing-Yano tensors and conserved "currents"

TL;DR

This paper develops new conserved currents from conformal Killing-Yano tensors, correcting previous formulas, and demonstrates their applications in black hole spacetimes like Kerr-Newman.

Contribution

It introduces novel CKYT-based conserved currents, corrects existing conformal transformation formulas, and explores their implications in gravitational physics.

Findings

New CKYT currents are constructed and characterized.

Corrected formulas for CKYTs under conformal transformations.

Application of currents to conserved charges in black hole spacetimes.

Abstract

In this paper we discuss the construction of conserved tensors (currents) involving conformal Killing-Yano tensors (CKYTs), generalising the corresponding constructions for Killing-Yano tensors (KYTs). As a useful preparation for this, but also of intrinsic interest, we derive identities relating CKYTs and geometric quantities. The behaviour of CKYTs under conformal transformations is also given, correcting formulae in the literature. We then use the identities derived to construct covariantly conserved ``currents''. We find several new CKYT currents and also include a known one by Penrose which shows that ``trivial'' currents are also useful. We further find that rank-$n$ currents based on rank-$n$ CKYTs $k$ must have a simple form in terms of $dk$. By construction, these currents are covariant under a general conformal rescaling of the metric. How currents lead to conserved charges is then illustrated using the Kerr-Newman and the C-metric in four dimensions. Separately, we study a rank-1 current, construct its charge and discuss its relation to the recently constructed Cotton current for the Kerr-Newman black hole.