VSI electromagnetic fields

TL;DR

This paper reviews recent results on VSI electromagnetic fields, highlighting their geometric properties, conditions for vanishing scalar invariants, and their universal applicability to various generalized electrodynamics theories.

Contribution

It summarizes the characterization of VSI p-forms in terms of type N, degenerate Kundt null directions, and invariance under Lie derivatives, emphasizing their universal solution property.

Findings

VSI p-forms are of type N with degenerate Kundt null directions.

VSI Maxwell fields can solve a wide class of generalized electrodynamics.

A subset of VSI fields exhibit universal solution properties.

Abstract

A $p$-form $F$ is VSI (i.e., all its scalar invariants of arbitrary order vanish) in a $n$-dimensional spacetime if and only if it is of type N, its multiple null direction $l$ is "degenerate Kundt", and $\pounds_{l}F=0$. This recent result is reviewed in the present contribution and its main consequences are summarized. In particular, a subset of VSI Maxwell fields possesses a universal property, i.e., they also solve (virtually) any generalized (non-linear and with higher derivatives) electrodynamics, possibly also coupled to Einstein's gravity.