Causal geometry of Einstein-Vacuum spacetimes with finite curvature flux

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Abstract

One of the central difficulties of settling the L2-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.

Original languageEnglish (US)
Pages (from-to)437-529
Number of pages93
JournalInventiones Mathematicae
Volume159
Issue number3
DOIs
StatePublished - Mar 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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