The time evolution of marginally trapped surfaces
Abstract
In previous work we have shown the existence of a dynamical horizon or marginally trapped tube (MOTT) containing a given strictly stable marginally outer trapped surface (MOTS). In this paper we show some results on the global behavior of MOTTs assuming the null energy condition. In particular we show that MOTSs persist in the sense that every Cauchy surface in the future of a given Cauchy surface containing a MOTS also must contain a MOTS. We describe a situation where the evolving outermost MOTS must jump during the coalescence of two seperate MOTSs. We furthermore characterize the behavior of MOTSs in the case that the principal eigenvalue vanishes under a genericity assumption. This leads to a regularity result for the tube of outermost MOTSs under the genericity assumption. This tube is then smooth up to finitely many jump times. Finally we discuss the relation of MOTSs to singularities of a space-time.
Keywords
Cite
@article{arxiv.0811.4721,
title = {The time evolution of marginally trapped surfaces},
author = {Lars Andersson and Marc Mars and Jan Metzger and Walter Simon},
journal= {arXiv preprint arXiv:0811.4721},
year = {2009}
}
Comments
21 pages. This revision corrects some typos and contains more detailed proofs than the original version