TY - JOUR
T1 - A fully anisotropic mechanism for formation of trapped surfaces in vacuum
AU - Klainerman, Sergiu
AU - Luk, Jonathan
AU - Rodnianski, Igor
N1 - 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
SN - 0020-9910
VL - 198
SP - 1
EP - 26
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 1
ER -