Outermost apparent horizons diffeomorphic to unit normal bundles

Abstract

Given a submanifold $S\subset {\mathbb{R}}^n$ of codimension at least three, we construct an asymptotically Euclidean Riemannian metric on ${\mathbb{R}}^n$ with nonnegative scalar curvature for which the outermost apparent horizon is diffeomorphic to the unit normal bundle of $S$.

v2: New proof of outer bound under weaker assumptions. The main theorem now holds in all dimensions. v3: Clarified definitions of "bounding", "enclosing" and "outermost" hypersurfaces. v4: Minor corrections