Non-existence of time-periodic vacuum space-times

Alexakis, Spyros; Schlue, Volker

doi:10.4310/jdg/1513998029

Non-existence of time-periodic vacuum space-times

Apr 17, 2015

62 pages

Published in:

J.Diff.Geom. 108 (2018) 1, 1-62

Published: 2018

e-Print:

1504.04592 [gr-qc]

DOI:

10.4310/jdg/1513998029

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Abstract: (Lehigh University)

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).

Note:

50 pages, 3 figures

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