On asymptotically flat solutions of Einstein's equations periodic in time I. Vacuum and electrovacuum solutions

TL;DR

This paper proves that any weakly-asymptotically-simple, analytic vacuum or electrovacuum solutions of Einstein's equations that are periodic in time must be stationary, extending previous results with a different approach.

Contribution

It demonstrates that time-periodic solutions under these conditions are necessarily stationary, using a new coordinate system and less restrictive gauge assumptions.

Findings

Periodic solutions are necessarily stationary.

The proof applies to vacuum and electrovacuum cases.

Uses a different coordinate system and gauge from previous work.

Abstract

By an argument similar to that of Gibbons and Stewart, but in a different coordinate system and less restrictive gauge, we show that any weakly-asymptotically-simple, analytic vacuum or electrovacuum solutions of the Einstein equations which are periodic in time are necessarily stationary.