Stationarity of asymptotically flat non-radiating electrovacuum spacetimes

TL;DR

This paper proves that non-radiating, asymptotically flat electrovacuum spacetimes are necessarily stationary near spatial infinity, implying that truly dynamical, time-periodic solutions cannot exist in this setting.

Contribution

It extends previous results on vacuum spacetimes to include electromagnetic fields, demonstrating stationarity under decay conditions for both gravitational and electromagnetic radiation.

Findings

Non-radiating solutions are stationary near infinity.

Dynamical time-periodic electrovacuum spacetimes do not exist.

Stationarity is established under decay conditions for Weyl and Faraday tensors.

Abstract

It is proven that a solution to the Einstein-Maxwell equations whose gravitational and electromagnetic radiation fields vanish is in fact stationary in a neighbourhood of spatial infinity. That is, if the Weyl and Faraday tensors decay suitably fast, then there exists a time-like Killing vector field in the region outside the bifurcate horizon of a sphere of sufficiently large radius. In particular, truly dynamical time-periodic electrovacuum spacetimes do not exist. This is an extension of earlier work by Alexakis and Schlue and Bi\v{c}\'{a}k, Sholtz and Tod to include electromagnetism.