On the existence and properties of helically symmetric systems

Abstract

By an argument similar to that of Gibbons and Stewart, but in a different coordinate system and less restrictive gauge, we showthat anyweakly asymptotically simple, analytic vacuum or electro-vacuum spacetime which is periodic in time is necessarily stationary. We generalized this theorem to the presence of scalar fields and, among other results, derived new expressions for the Bondi mass in this case. Here we summarize these results and also briefly discuss some new considerations concerning the periodic solutions within linearized theory of gravity.