TRAPPED SURFACES IN VACUUM SPACETIMES

An earlier construction by the authors of sequences of globally regula r, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is exten ded, from the time symmetric case considered previously, to the case o f maximal slices. The resulting theorem shows rigourously that there e xists a large class of initial configurations for non-time symmetric, pure gravitational waves satisfying the assumptions of the Penrose sin gularity theorem, and so must have a singularity to the future.