Einstein-Maxwell fields with vanishing higher-order corrections

Abstract

We obtain a full characterization of Einstein-Maxwell $p$-form solutions $(\mathbf{g},\mathbf{F})$ in $D$-dimensions for which all higher-order corrections vanish identically. These thus simultaneously solve a large class of Lagrangian theories including both modified gravities and (possibly non-minimally coupled) modified electrodynamics. Specifically, both $\mathbf{g}$ and $\mathbf{F}$ are fields with vanishing scalar invariants and further satisfy two simple tensorial conditions. They describe a family of gravitational and electromagnetic plane-fronted waves of the Kundt class and of Weyl type III (or more special). The local form of $(\mathbf{g},\mathbf{F})$ and a few examples are also provided.

v2: a few minor changes in the text and proof of lemma B.6 slightly improved, results unchanged