New Examples of Marginally Trapped Surfaces and Tubes in Warped Spacetimes

Abstract

In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf map. The utility of this method is illustrated by providing marginally trapped surfaces crossing expanding and collapsing regions of a closed FLRW spacetime. The approach introduced in this paper is also extended to twisted spaces.

20 pages

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• Marginally Outer Trapped Tori in Black Hole Spacetimes
• Vacuum initial data on ${\mathbb{S}}^3$ from Killing vectors
• Extremal and weakly trapped submanifolds in Generalized Robertson-Walker spacetimes
• On complete trapped submanifolds in globally hyperbolic spacetimes
• Rigidity and non-existence of spacelike submanifolds with causal mean curvature vector field in spacetimes and the Cauchy problem in General Relativity
• Compact Mean Convex Hypersurfaces and the Fundamental Group of Manifolds with Nonnegative Ricci Curvature