Abstract
We determine the class of p-forms that possess vanishing scalar invariants (VSIs) at arbitrary order in an n-dimensional spacetime. Namely, we prove that is a VSI if and only if if it is of type N, its multiple null direction is ‘degenerate Kundt’, and . 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.
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