Open Access
2018 Non-existence of time-periodic vacuum space-times
Spyros Alexakis, Volker Schlue
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J. Differential Geom. 108(1): 1-62 (2018). DOI: 10.4310/jdg/1513998029


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 Bičák, Scholtz, and Tod (2010). The proof relies on extending a suitably constructed “candidate” Killing vector field from null infinity, via Carleman-type estimates obtained in Alexakis, Schlue, and Shao (2013).


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Spyros Alexakis. Volker Schlue. "Non-existence of time-periodic vacuum space-times." J. Differential Geom. 108 (1) 1 - 62, 2018.


Received: 24 April 2015; Published: 2018
First available in Project Euclid: 23 December 2017

zbMATH: 06846973
MathSciNet: MR3743702
Digital Object Identifier: 10.4310/jdg/1513998029

Rights: Copyright © 2018 Lehigh University

Vol.108 • No. 1 • 2018
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