Codimension two marginally trapped submanifolds in Robertson-Walker spaces

TL;DR

This paper characterizes codimension two marginally trapped submanifolds in Robertson-Walker spaces using algebraic equations, proves abundant local solutions, and refines descriptions for specific cases like null acceleration curves.

Contribution

It provides a new local algebraic characterization of marginally trapped submanifolds in Robertson-Walker spaces and explores special cases with null second fundamental form.

Findings

Existence of many local solutions for marginally trapped submanifolds.

Characterization of curves with null acceleration in these spaces.

Refined description for submanifolds with null second fundamental form.

Abstract

We give a local characterization of codimension two submanifolds which are marginally trapped in Robertson-Walker spaces, in terms of an algebraic equation to be satisfied by the height function. We prove the existence of a large number of local solutions. We refine the description in the case of curves with null acceleration in three-dimensional spaces Robertson-Walker spaces, and in the case of codimension two submanifolds whose second fundamental form is null