A sharp counterexample to local existence of low regularity solutions to Einstein equations in wave coordinates

Abstract

We give a sharp counterexample to local existence of low regularity solutions to Einstein equations in wave coordinates. We show that there are initial data in $H^2$ satisfying the wave coordinate condition such that there is no solution in $H^2$ to Einstein equations in wave coordinates for any positive time. This result is sharp since Klainerman-Rodnianski and Smith-Tataru proved existence for the same equations with slightly more regular initial data.

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Authors

Boris Ettinger

Hans Lindblad

Johns Hopkins University, Baltimore, MD