Universal electromagnetic fields

TL;DR

This paper characterizes universal electromagnetic fields that solve a wide class of generalized electrodynamics equations in various spacetimes, identifying conditions under which null fields are universal and exploring their invariants.

Contribution

It provides a sufficient condition for null fields to be universal in Kundt spacetimes and discusses the invariants of universal 2-forms in four dimensions.

Findings

Null F solving Maxwell's equations in Kundt spacetimes are universal.

Universal 2-forms in 4D have constant scalar invariants.

Examples of universal fields in specific Kundt backgrounds are presented.

Abstract

We study universal electromagnetic (test) fields, i.e., p-forms fields F that solve simultaneously (virtually) any generalized electrodynamics (containing arbitrary powers and derivatives of F in the field equations) in n spacetime dimensions. One of the main results is a sufficient condition: any null F that solves Maxwell's equations in a Kundt spacetime of aligned Weyl and traceless-Ricci type III is universal (in particular thus providing examples of p-form Galileons on curved Kundt backgrounds). In addition, a few examples in Kundt spacetimes of Weyl type II are presented. Some necessary conditions are also obtained, which are particularly strong in the case n=4=2p: all the scalar invariants of a universal 2-form in four dimensions must be constant, and vanish in the special case of a null F .