Outermost apparent horizons diffeomorphic to unit normal bundles

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 $S$.