A fully anisotropic mechanism for formation of trapped surfaces in vacuum
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Rodnianski_A fully.pdf
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Author(s)
Klainerman, Sergiu
Luk, Jonathan
Rodnianski, Igor
Date Issued
January 2014
Journal
Inventiones Mathematicae
Publisher
Springer-Verlag
Citation
Klainerman, Sergiu, Jonathan Luk, and Igor Rodnianski. “A Fully Anisotropic Mechanism for Formation of Trapped Surfaces in Vacuum.” Invent. Math. 198, no. 1 (January 8, 2014): 1–26.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00222-013-0496-6
