Existence of Outermost Apparent Horizons with Product of Spheres Topology

Abstract

In this paper we find new examples of Riemannian manifolds with nonspherical apparent horizon, in dimensions four and above. More precisely, for any n, m ≥ 1, we construct asymptotically flat, scalar flat Riemannian manifolds containing smooth outermost minimal hypersurfaces with topology Sn × S. In the context of general relativity these hypersurfaces… (More)

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