NON-EXISTENCE OF TIME-PERIODIC VACUUM SPACE-TIMES
Spyros Alexakis, Volker Schlue
JOURNAL OF DIFFERENTIAL GEOMETRY | INT PRESS BOSTON, INC | Published : 2018
We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity. Our result applies under physically relevant regularity assumptions purely at the level of the initial data. In particular, our work removes the assumption of analyticity up to null infinity in Biˇc´ak, Scholtz, and Tod . The proof relies on extending a suitably constructed “candidate” Killing vector field from null infinity, via Carlemantype estimates obtained in Alexakis, Schlue, and Shao .