Einstein-Maxwell fields as solutions of Einstein gravity coupled to conformally invariant non-linear electrodynamics

Fuente: arXiv
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Main Author: Ortaggio, Marcello
Format: Preprint
Published: 2025
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author Ortaggio, Marcello
author_facet Ortaggio, Marcello
contents We study Einstein-Maxwell (non-null) sourcefree configurations that can be extended to any conformally invariant non-linear electrodynamics (CINLE) by a constant rescaling of the electromagnetic field. We first obtain a criterion which characterizes such extendable solutions in terms either of the electromagnetic invariants, or (equivalently) of the canonical Newman-Penrose form of the self-dual Maxwell field. This is then used to argue that all static configurations are extendable (more generally, all configurations admitting a non-null twistfree Killing vector field). One can thus draw from the extensive literature to straightforwardly extend to CINLE various known exact solutions, whereby the duality invariance of the Einstein-Maxwell theory allows for dyonic solutions even in more general theories. This is illustrated by a few explicit examples, including the homogeneous $Λ<0$ universe of Ozsváth, a black hole in the universe of Levi-Civita, Bertotti and Robinson, a generalization of the charged $C$-metric, and non-expanding gravitational waves in the Bonnor-Melvin background.
format Preprint
id arxiv_https___arxiv_org_abs_2511_13665
institution arXiv
publishDate 2025
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spellingShingle Einstein-Maxwell fields as solutions of Einstein gravity coupled to conformally invariant non-linear electrodynamics
Ortaggio, Marcello
General Relativity and Quantum Cosmology
High Energy Physics - Theory
We study Einstein-Maxwell (non-null) sourcefree configurations that can be extended to any conformally invariant non-linear electrodynamics (CINLE) by a constant rescaling of the electromagnetic field. We first obtain a criterion which characterizes such extendable solutions in terms either of the electromagnetic invariants, or (equivalently) of the canonical Newman-Penrose form of the self-dual Maxwell field. This is then used to argue that all static configurations are extendable (more generally, all configurations admitting a non-null twistfree Killing vector field). One can thus draw from the extensive literature to straightforwardly extend to CINLE various known exact solutions, whereby the duality invariance of the Einstein-Maxwell theory allows for dyonic solutions even in more general theories. This is illustrated by a few explicit examples, including the homogeneous $Λ<0$ universe of Ozsváth, a black hole in the universe of Levi-Civita, Bertotti and Robinson, a generalization of the charged $C$-metric, and non-expanding gravitational waves in the Bonnor-Melvin background.
title Einstein-Maxwell fields as solutions of Einstein gravity coupled to conformally invariant non-linear electrodynamics
topic General Relativity and Quantum Cosmology
High Energy Physics - Theory
url https://arxiv.org/abs/2511.13665