A Rainich-like approach to the Killing-Yano tensors

TL;DR

This paper solves the Rainich problem for Killing-Yano tensors, providing conditions for their structure and relating them to Maxwell fields, which aids in understanding spacetimes with these first integrals.

Contribution

It offers a Rainich-like characterization for Killing-Yano tensors and extends the analysis to conformal Killing-Yano tensors, linking geometric structures to Maxwell fields.

Findings

Necessary and sufficient conditions for Killing-Yano tensors

Principal 2-planes define a Maxwellian structure

Maxwell fields associated with Killing-Yano tensors

Abstract

The Rainich problem for the Killing-Yano tensors posed by Collinson \cite{col} is solved. In intermediate steps, we first obtain the necessary and sufficient conditions for a 2+2 almost-product structure to determine the principal 2--planes of a skew-symmetric Killing-Yano tensor and then we give the additional conditions on a symmetric Killing tensor for it to be the square of a Killing-Yano tensor.We also analyze a similar problem for the conformal Killing-Yano and the conformal Killing tensors. Our results show that, in both cases, the principal 2--planes define a maxwellian structure. The associated Maxwell fields are obtained and we outline how this approach is of interest in studying the spacetimes that admit these kind of first integrals of the geodesic equation.