Outer trapped surfaces are dense near MOTSs

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.

14 pages, minor rewordings

References in corpus (3)

• Local existence of dynamical and trapping horizons
• KIDs are non-generic
• The area of horizons and the trapped region

Cited by in corpus (2)

• A note on the positive mass theorem with boundary
• On the genericity of singularities in spacetimes with weakly trapped submanifolds