Einstein-Maxwell fields as solutions of higher-order theories

TL;DR

This paper identifies specific Einstein-Maxwell solutions that remain valid across a wide range of higher-order gravity theories, characterized by their unique electromagnetic and gravitational wave properties.

Contribution

It provides a full characterization of universal Einstein-Maxwell solutions applicable to virtually any modified gravity coupled with electrodynamics, including non-null and null fields.

Findings

Universal solutions reduce higher-order corrections to rescaling of constants.

Characterization of gravitational waves in Levi-Civita--Bertotti--Robinson backgrounds.

Solutions exemplified for Born-Infeld, ModMax, and Horndeski electrodynamics.

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.