On the topology of untrapped surfaces

TL;DR

This paper proves that strictly stable untrapped surfaces in higher-dimensional spacetimes share the same topological properties as marginally outer trapped surfaces, extending previous black hole topology results.

Contribution

It introduces a new proof linking the topology of untrapped surfaces to that of MOTSs and defines a quasi-local notion of outward and inward directions for these surfaces.

Findings

Strictly stable untrapped surfaces have the same topological properties as MOTSs.

A new proof method for black hole topology theorems is presented.

A quasi-local notion of outward/inward directions for surfaces is introduced.

Abstract

Recently a simple proof of the generalizations of Hawking's black hole topology theorem and its application to topological black holes for higher dimensional ($n\geq 4$) spacetimes was given \cite{rnew}. By applying the associated new line of argument it is proven here that strictly stable untrapped surfaces do possess exactly the same topological properties as strictly stable marginally outer trapped surfaces (MOTSs) are known to have. In addition, a quasi-local notion of outwards and inwards pointing spacelike directions--applicable to untrapped and marginally trapped surfaces--is also introduced.