, Volume 159, Issue 3, pp 437-529
Date: 22 Dec 2004

Causal geometry of Einstein-Vacuum spacetimes with finite curvature flux

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Abstract

One of the central difficulties of settling the L 2-bounded curvature conjecture for the Einstein-Vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity. In this paper we show how to circumvent this difficulty by showing that the geometry of null hypersurfaces of Enstein-Vacuum spacetimes can be controlled in terms of initial data and the total curvature flux through the hypersurface.