New currents with Killing-Yano tensors

TL;DR

This paper explores new geometric relations involving Killing-Yano tensors, introduces novel conserved currents, and discusses their implications for conserved charges and matter coupling in gravitational theories.

Contribution

It presents new relations involving Riemann, Ricci, and Einstein tensors for geometries with Killing-Yano tensors and introduces novel conserved currents based on these tensors.

Findings

Derived conditions for geometries to admit Killing-Yano tensors.

Introduced new conserved currents involving Killing-Yano tensors.

Analyzed conserved charges and their dependence on background geometry.

Abstract

New relations involving the Riemann, Ricci and Einstein tensors that have to hold for a given geometry to admit Killing-Yano tensors are described. These relations are then used to introduce novel conserved "currents" involving such Killing-Yano tensors. For a particular current based on the Einstein tensor, we discuss the issue of conserved charges and consider implications for matter coupled to gravity. The condition on the background geometry to allow asymptotic conserved charges for a current introduced by Kastor and Traschen is found and a number of other new aspects of this current are commented on. In particular we show that it vanishes for rank $(D-1)$ Killing-Yano tensors in $D$ dimensions.