Existence of outermost apparent horizons with product of spheres topology

Abstract

In this paper we find new examples of Riemannian manifolds with outermost apparent horizons with nonspherical topology, in dimensions four and above. More precisely, for any $n,m\ge1$, we construct asymptotically flat, scalar flat Riemannian manifolds containing smooth outermost minimal hypersurfaces with topology $S^n\times S^{m+1}$. In the context of general relativity these hypersurfaces correspond to outermost apparent horizons of black holes.