English

Outermost apparent horizons diffeomorphic to unit normal bundles

Differential Geometry 2020-08-05 v4 General Relativity and Quantum Cosmology

Abstract

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

Keywords

Cite

@article{arxiv.1606.08418,
  title  = {Outermost apparent horizons diffeomorphic to unit normal bundles},
  author = {Mattias Dahl and Eric Larsson},
  journal= {arXiv preprint arXiv:1606.08418},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-22T14:35:34.730Z