TY - JOUR
T1 - A fully anisotropic mechanism for formation of trapped surfaces in vacuum
AU - Klainerman, Sergiu
AU - Luk, Jonathan
AU - Rodnianski, Igor
N1 - Funding Information:
We would like to thank Demetrios Christodoulou for his helpful suggestions on a previous version of the manuscript. We would also like to thank Pin Yu, Ovidiu Savin and Stefanos Aretakis for helpful remarks and useful discussions. S. Klainerman would like to thank the Fondation SMP for the support of this work. S. Klainerman is supported by the NSF Grant DMS-0901250. J. Luk is supported by the NSF Postdoctoral Fellowship DMS-1204493. I. Rodnianski is supported by the NSF Grant DMS-1001500. S. Klainerman and I. Rodnianski are also supported by the FRG Grant DMS-1065710.
Publisher Copyright:
© 2013, Springer-Verlag Berlin Heidelberg.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - 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.
AB - 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.
KW - 35Q76
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U2 - 10.1007/s00222-013-0496-6
DO - 10.1007/s00222-013-0496-6
M3 - Article
AN - SCOPUS:84908207382
SN - 0020-9910
VL - 198
SP - 1
EP - 26
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 1
ER -