A fully anisotropic mechanism for formation of trapped surfaces in vacuum

TL;DR

This paper introduces a new anisotropic criterion for forming trapped surfaces in vacuum spacetimes, extending previous uniform conditions to localized null data, and combines Christodoulou's mechanism with a novel deformation process.

Contribution

It provides a more general, localized condition for trapped surface formation, advancing understanding of gravitational collapse in vacuum.

Findings

New anisotropic criterion for trapped surfaces

Extension of Christodoulou's results to localized data

Combination of formation mechanism with deformation process

Abstract

We present a new, fully anisotropic, criterion for formation of trapped surfaces in vacuum. More precisely we provide conditions on null data, concentrated in a neighborhood of a short null geodesic segment (possibly flat everywhere else) whose future development contains a trapped surface. This extends considerably the previous result of Christodoulou \cite{Chr:book} 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.