Nonlinear electromagnetic fields in strictly stationary spacetimes

We prove two theorems which imply that any 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. First theorem holds in static spacetimes and is independent of gravitational part of the action, as long as the coupling of electromagnetic field to the gravitational field is minimal. 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.

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