A fully anisotropic mechanism for formation of trapped surfaces in vacuum

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Abstract

We present a new, fully anisotropic, criterion for formation of trapped surfaces in vacuum. More precisely we provide local conditions on null data, concentrated in a neighborhood of a short null geodesic segment (possibly flat in all other directions) whose future development contains a trapped surface. This extends considerably the previous result of Christodoulou (Monographs in Mathematics. European Mathematical Society, Switzerland, 2009) which required instead a uniform condition along all null geodesic generators. To obtain our result we combine Christodoulou’s mechanism for the formation of a trapped surface with a new deformation process which takes place along incoming null hypersurfaces.

Original languageEnglish (US)
Pages (from-to)1-26
Number of pages26
JournalInventiones Mathematicae
Volume198
Issue number1
DOIs
StatePublished - Oct 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • 35Q76

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