arXiv subjects
Publications and source records attributed to David Parlongue.
We revisit in this article results of Klainerman and Rodnianski on a geometric breakdown criterion for Einstein vacuum spacetimes. We take advantage of the use of a time-harmonic transversal gauge to give a localized version (in space and time) of this result.
We prove in this note that local geometric uniqueness holds true without loss of regularity for Einstein equations coupled with a large class of matter models. We thus extend the Planchon-Rodnianski uniqueness theorem for vacuum spacetimes. In a second part of this note, we investigate the question of local regularity of spacetimes under geometric bounds.
We will give in this paper the proof of an integral breakdown criterion for Einstein vacuum equations. In a recent article of S.Klainerman and I.Rodnianski a new breakdown criterion was proved as a result of a sequence of articles involving new techniques. However, in this article, the authors mentioned that it was likely possible to prove a sharper result involving an integral condition instead of a pointwise one. This paper is concerned with giving the proof of this improvement. Moreover the proof of this breakdown criterion was written in the original article for a foliation of constant mean curvature, we will present it here for a maximal foliation which leads to some difficulties due to the non-compacity of the leaves of such a foliation and the use of weighted Sobolev norms.