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Non-existence of time-periodic vacuum spacetimes in general relativity

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If you have a question about this talk, please contact Harsha Hutridurga.

In general relativity, it is expected that a gravitating system cannot display time-periodic dynamics. This is in contrast to Newton’s theory of gravity, which allows for periodic motion, and corresponding gravitational fields. I will explain how the development of certain uniqueness theorems for linear waves, obtained jointly with Spyros Alexakis and Arick Shao, has led to a proof that any asymptotically flat time-periodic solution to the Einstein equations must be time-independent, at least far away from the sources. Thus genuinely time-periodic vacuum spacetimes do not exist. I will relate the discussion to the so-called final state conjecture, and the soliton resolution conjecture for dispersive p.d.e.’s.

This talk is part of the Partial Differential Equations seminar series.

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