On the topology of untrapped surfaces

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 ($n\ge 4$) 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.

9 pages, no figures

References in corpus (3)

• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• A simple proof of the recent generalisations of Hawking's black hole topology theorem
• Some remarks on the size of bodies and black holes

Cited by in corpus (3)

• Gravitational collapse and topology change in spherically symmetric dynamical systems
• On the construction of Riemannian three-spaces with smooth inverse mean curvature foliation
• Geometric inequalities in spherically symmetric spacetimes