Outermost apparent horizons diffeomorphic to unit normal bundles

TL;DR

This paper constructs specific asymptotically Euclidean metrics with nonnegative scalar curvature on ^n, where the outermost apparent horizon is diffeomorphic to the unit normal bundle of a given submanifold of codimension at least three.

Contribution

It introduces a method to produce asymptotically Euclidean metrics with prescribed outermost apparent horizons diffeomorphic to unit normal bundles of submanifolds.

Findings

Successfully constructs metrics with desired horizon topology.

Demonstrates the existence of horizons diffeomorphic to complex normal bundles.

Provides a new approach to horizon topology in geometric analysis.

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 $S$.