Einstein-Maxwell fields as solutions of higher-order theories
Abstract
We study four-dimensional Einstein-Maxwell fields for which any higher-order corrections to the field equations effectively reduces to just a rescaling of the gravitational and the cosmological constant. These configurations are thus simultaneous solutions of (virtually) any modified theory of gravity coupled (possibly non-minimally) to any electrodynamics. In the case of non-null electromagnetic fields we provide a full characterization of such universal solutions, which correspond to a family of gravitational waves propagating in universes of the Levi-Civita--Bertotti--Robinson type. For null fields we first obtain a set of general necessary conditions, and then a full characterization for a special subfamily, which turns out to represent electromagnetic waves accompanied by pure radiation in the (anti-)Nariai background. The results are exemplified for the case of Born-Infeld, ModMax and Horndeski electrodynamics.
Keywords
Cite
@article{arxiv.2205.14392,
title = {Einstein-Maxwell fields as solutions of higher-order theories},
author = {Marcello Ortaggio},
journal= {arXiv preprint arXiv:2205.14392},
year = {2023}
}
Comments
31 pages. v2: a few comments added, Einstein-Weyl-ModMax theory as a new example, typos fixed, improvements to the text, refs. added (main results unchanged; matches the published version)