Outer trapped surfaces are dense near MOTSs

TL;DR

This paper demonstrates that in vacuum initial data with a marginally outer trapped surface and a no KIDs condition, it is possible to perturb the data so that the surface becomes strictly outer trapped, indicating generic initial data with MOTSs lead to geodesic incompleteness.

Contribution

It introduces a perturbation method to convert MOTSs into strictly outer trapped surfaces under specific conditions, advancing understanding of initial data's role in spacetime singularities.

Findings

Perturbation can make MOTSs strictly outer trapped

Generic initial data with MOTSs imply geodesic incompleteness

Provides a link between initial data properties and spacetime singularities

Abstract

We show that any vacuum initial data set containing a marginally outer trapped surface S and satisfying a "no KIDs" condition can be perturbed near S so that S becomes strictly outer trapped in the new vacuum initial data set. This, together with the results in [9], gives a precise sense in which generic initial data containing marginally outer trapped surfaces lead to geodesically incomplete spacetimes.