Aligned electric and magnetic Weyl fields

TL;DR

This paper characterizes spacetimes with aligned electric and magnetic Weyl fields, providing invariant descriptions, analyzing null vectors, and extending results on purely magnetic solutions across Petrov types.

Contribution

It offers a new invariant characterization of such spacetimes and extends the understanding of their properties and the existence of purely magnetic solutions.

Findings

Aligned electric and magnetic Weyl fields are characterized invariantly.

Null vectors associated with these fields are studied across Petrov types.

Extensions of non-existence results for purely magnetic solutions are presented.

Abstract

We analyze the spacetimes admitting a direction for which the relative electric and magnetic Weyl fields are aligned. We give an invariant characterization of these metrics and study the properties of its Debever null vectors. The directions 'observing' aligned electric and magnetic Weyl fields are obtained for every Petrov type. The results on the no existence of purely magnetic solutions are extended to the wider class having homothetic electric and magnetic Weyl fields.