Electromagnetic fields with vanishing scalar invariants

Abstract

We determine the class of $p$-forms $F$ which possess vanishing scalar invariants (VSI) at arbitrary order in a $n$-dimensional spacetime. Namely, we prove that $F$ is VSI if and only if it is of type N, its multiple null direction $l$ is "degenerate Kundt", and ${\nabla }_{l}F=0$. The result is theory-independent. Next, we discuss the special case of Maxwell fields, both at the level of test fields and of the full Einstein-Maxwell equations. These describe electromagnetic non-expanding waves propagating in various Kundt spacetimes. We further point out that a subset of these solutions 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.

v2: a few comments added (including new Proposition A3), minor corrections, main results unchanged. 24 pages

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• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
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• Higher dimensional VSI spacetimes
• General Kundt spacetimes in higher dimensions
• Higher dimensional Kerr-Schild spacetimes
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• Supersymmetric gyratons in five dimensions
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• Universal electromagnetic fields
• Einstein-Maxwell fields as solutions of higher-order theories
• Universal spacetimes in four dimensions
• Gyratons in the Robinson-Trautman and Kundt classes
• Kerr-Schild double copy for Kundt spacetimes of any dimension
• Static and radiating dyonic black holes coupled to conformally invariant electrodynamics in higher dimensions
• Kundt spacetimes in the Einstein-Gauss-Bonnet theory
• Generalizations and challenges for the spacetime block-diagonalization
• Kerr-Schild-Kundt Metrics in Generic Gravity Theories with Modified Horndeski Couplings
• Einstein-Maxwell fields with vanishing higher-order corrections
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• Lovelock vacua with a recurrent null vector field
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• All non-expanding gravitational waves in $D$-dimensional (anti-)de Sitter space
• Gauge fields with vanishing scalar invariants
• Almost Universal Metrics
• Einstein-Yang-Mills fields immune to quantum corrections