Nonlinear electromagnetic fields in strictly stationary spacetimes

Abstract

We prove two theorems which imply that any stationary nonlinear electromagnetic field obeying a dominant energy condition in a strictly stationary, everywhere regular, asymptotically flat spacetime must be either trivial or a stealth field. The first theorem holds in static spacetimes and is independent of the gravitational part of the action, as long as the coupling of the electromagnetic field to the gravitational field is minimal. The second theorem assumes Einstein--Hilbert gravitational action and relies on the positive energy theorem, but does not assume that the spacetime metric is static. In addition, we discuss possible generalizations of these results, to theories with charged matter, as well as higher-dimensional nonlinear electromagnetic fields.

8.1 pages (two columns); ver.2: version accepted for publication in Physical Review D (several references added and some typos corrected)

References in corpus (18)

• Higher-dimensional black holes with a conformally invariant Maxwell source
• Higher-dimensional charged black holes solutions with a nonlinear electrodynamics source
• Asymptotic Reissner-Nordstrom black holes
• Black holes and gravitational waves sourced by non-linear duality rotation-invariant conformal electromagnetic matter
• Black hole thermodynamics in the presence of nonlinear electromagnetic fields
• Comment on "Construction of regular black holes in general relativity"
• Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields
• Traversable wormholes coupled to nonlinear electrodynamics
• On the inexistence of solitons in Einstein-Maxwell-scalar models
• Asymptotically anomalous black hole configurations in gravitating nonlinear electrodynamics
• Symmetry inheritance of scalar fields
• Can the power Maxwell nonlinear electrodynamics theory remove the singularity of electric field of point-like charges at their locations?
• Conditions for nonexistence of static or stationary, Einstein-Maxwell, non-inheriting black-holes
• Nonlinear electromagnetic fields and symmetries
• Constraints on the symmetry noninheriting scalar black hole hair
• Asymptotic behaviour of Maxwell fields in higher dimensions
• Stationary spacetimes with time-dependent real scalar fields
• Lichnerowicz-Type Theorems for Self-gravitating Systems with Nonlinear Electromagnetic Fields

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• Maximally symmetric nonlinear extension of electrodynamics and charged particles
• Constraints on singularity resolution by nonlinear electrodynamics
• Exploring Nonlinear Electrodynamics Theories: Shadows of Regular Black Holes and Horizonless Ultra-Compact Objects
• The covariant approach to static spacetimes in Einstein and extended gravity theories
• Conundrum of regular black holes with nonlinear electromagnetic fields
• Weighing the curvature invariants