On the formation of trapped surfaces (Q444055)

This heavy paper of 123 journal pages has one single purpose: to give a simpler proof of the result presented within 589 pages in 2009 [\textit{D. Christodoulou}, The formation of black holes in general relativity. EMS Monographs in Mathematics. Zürich: European Mathematical Society (EMS) (2009; Zbl 1197.83004)]. The mentioned result has the following structure: It proves the existence of a non-empty open set of regular initial conditions on a finite outgoing null hypersurface leading to the formation of a trapped surface in the corresponding vacuum space-time, thus, to the formation of a black hole. NEWLINENEWLINENEWLINE NEWLINEThe main method is to use a double null foliation of the space-time, apply the Einstein field equation and the Bianchi identities, and proceed with a huge number of integral inequalities. The main difference of the present paper to almost all other papers dealing with the formation of black holes is the fact that no symmetry of the system is assumed from the beginning.