Trapped surfaces due to concentration of gravitational radiation

Abstract

Sequences of nonsingular, asymptotically flat initial data for general relativity (GR) in vacuo, called critical sequences, are defined which approach the strong-field limit of GR in a precise sense. It is proven to Penrose, the spacetimes evolving from all such configurations must develop singularities. In the course of the proof a new and conceptually simple proof of the positivity of the Arnowitt-Deser-Misner mass in the strong-field regime is obtained.