Journal article

NON-EXISTENCE OF TIME-PERIODIC VACUUM SPACE-TIMES

Spyros Alexakis, Volker Schlue

JOURNAL OF DIFFERENTIAL GEOMETRY | INT PRESS BOSTON, INC | Published : 2018

Abstract

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 [2010]. The proof relies on extending a suitably constructed “candidate” Killing vector field from null infinity, via Carlemantype estimates obtained in Alexakis, Schlue, and Shao [2013].

University of Melbourne Researchers