Existence of outermost apparent horizons with product of spheres topology

In this paper we construct the first examples of $(n+m+2)$-dimensional asymptotically flat Riemannian manifolds withnon-negative scalar curvature that have outermost minimalhypersurfaces with non-spherical topology for $n,m\ge 1$.

The outermost minimal hypersurfaces are, topologically,$S^n\times S^{m+1}$. In the context of general relativitythese hypersurfaces correspond to outermost apparenthorizons of black holes.

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Published 1 January 2008