Local existence of dynamical and trapping horizons

TL;DR

This paper proves the local existence of dynamical and trapping horizons in spacetimes with a given foliation, establishing conditions for their smoothness and causal properties, and explores stability and bounding properties of marginally outer trapped surfaces.

Contribution

It introduces a new proof of local horizon existence based on stability conditions and analyzes their causal nature under weak energy assumptions.

Findings

Horizon surfaces are contained in the spacetime foliation under stability.

Under weak energy conditions, horizons are either achronal or spacelike.

Relations between bounding and stability of marginally outer trapped surfaces are discussed.

Abstract

Given a spacelike foliation of a spacetime and a marginally outer trapped surface S on some initial leaf, we prove that under a suitable stability condition S is contained in a ``horizon'', i.e. a smooth 3-surface foliated by marginally outer trapped slices which lie in the leaves of the given foliation. We also show that under rather weak energy conditions this horizon must be either achronal or spacelike everywhere. Furthermore, we discuss the relation between ``bounding'' and ``stability'' properties of marginally outer trapped surfaces.