Nonlinear electromagnetic fields in strictly stationary spacetimes

TL;DR

This paper proves theorems showing that in strictly stationary, asymptotically flat spacetimes, nonlinear electromagnetic fields under certain conditions are either trivial or stealth, with implications for gravitational and electromagnetic theory.

Contribution

It establishes new theorems constraining nonlinear electromagnetic fields in stationary spacetimes, independent of gravitational action and using positive energy arguments.

Findings

Nonlinear electromagnetic fields must be trivial or stealth in certain stationary spacetimes.

Theorems apply to static and non-static cases, with minimal coupling and Einstein-Hilbert gravity.

Results suggest limitations on electromagnetic configurations in general relativity.

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.