On marginally outer trapped surfaces in stationary and static spacetimes

TL;DR

This paper proves that marginally outer trapped surfaces cannot exist in the exterior regions where the stationary or static Killing vectors are timelike, based on initial data and energy conditions, extending previous results without assuming spacetime existence.

Contribution

It establishes new constraints on the location of marginally outer trapped surfaces in stationary and static spacetimes at an initial data level, without requiring spacetime assumptions.

Findings

MOTS cannot lie in the exterior timelike region in stationary spacetimes with null energy condition.

In static spacetimes, MOTS cannot penetrate into the exterior timelike region.

Results are proven at the initial data level, independent of spacetime existence.

Abstract

In this paper we prove that for any spacelike hypersurface containing an untrapped barrier in a stationary spacetime satisfying the null energy condition, any marginally outer trapped surface cannot lie in the exterior region where the stationary Killing vector is timelike. In the static case we prove that any marginally outer trapped surface cannot penetrate into the exterior region where the static Killing vector is timelike. In fact, we prove these result at an initial data level, without even assuming existence of a spacetime. The proof relies on a powerful theorem by Andersson and Metzger on existence of an outermost marginally outer trapped surface.