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.

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)

References in corpus (9)

• A non-linear duality-invariant conformal extension of Maxwell's equations
• Nonlinear electrodynamics with the maximum allowable symmetries
• Black holes and gravitational waves sourced by non-linear duality rotation-invariant conformal electromagnetic matter
• AdS Waves as Exact Solutions to Quadratic Gravity
• Gyratons on direct-product spacetimes
• Impulsive waves in electrovac direct product spacetimes with Lambda
• Universal spacetimes in four dimensions
• Kerr-Schild-Kundt Metrics in Generic Gravity Theories with Modified Horndeski Couplings
• Kerr-Schild-Kundt Metrics in Generic Einstein-Maxwell Theories

Cited by in corpus (6)

• Maximally symmetric nonlinear extension of electrodynamics and charged particles
• Topological Mod(A)Max AdS black holes
• Generalizations and challenges for the spacetime block-diagonalization
• Thermal and Optical Signatures of Einstein-Dyonic ModMax Black Holes with GUP and Plasma Modifications
• Cosmological Tensions with Non-Extensive Entropic Cosmology: A Modified Stress-Energy Approach
• Accelerating electrically charged ModMax black hole solutions in $F(R)$ gravity