Trapped Surfaces in Vacuum Spacetimes

TL;DR

This paper extends previous work on initial data for Einstein vacuum equations to maximal slices, demonstrating the existence of configurations that lead to singularities due to trapped surfaces in non-time symmetric gravitational waves.

Contribution

It generalizes earlier constructions from time symmetric to maximal slices, providing a rigorous proof of trapped surfaces leading to singularities in a broader class of initial data.

Findings

Existence of initial data with trapped surfaces in non-time symmetric vacuum spacetimes.

Proof that such data satisfy Penrose's conditions for singularity formation.

Demonstration of singularity development in these configurations.

Abstract

An earlier construction by the authors of sequences of globally regular, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is extended, from the time symmetric case considered previously, to the case of maximal slices. The resulting theorem shows rigorously that there exists a large class of initial configurations for non-time symmetric pure gravitational waves satisfying the assumptions of the Penrose singularity theorem and so must have a singularity to the future.