Compactness Theorems and Degree Theory for MOTS

TL;DR

This paper establishes area and curvature estimates for MOTS, leading to a compactness theorem that facilitates existence proofs for embedded MOTS using degree theory in initial data sets.

Contribution

It introduces new compactness and degree theory results for MOTS under specific initial data conditions, advancing the understanding of their geometric properties.

Findings

Proves area and curvature estimates for MOTS.

Derives a compactness theorem for MOTS.

Adapts degree theory to prove existence of embedded MOTS.

Abstract

We prove in this paper that, under suitable coinditions on an initial data set, we can obtain Area and Curvature Estimates for simple marginally outer trapped surfaces (or MOTS). Using this estimates, we derive a Compactness Theorem for MOTS. Moreover, the Compactness Theorem will allow us to adapt the recent Degree Theory of H. Rosenberg and G. Smith for proving existence results for embedded MOTS in suitable compact initial data sets