A fully anisotropic mechanism for formation of trapped surfaces in vacuum

作者：Klainerman Sergiu^*; Luk Jonathan; Rodnianski Igor

来源：Inventiones Mathematicae, 2014, 198(1): 1-26.

DOI：10.1007/s00222-013-0496-6

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.

• 出版日期2014-10