# Existence of outermost apparent horizons with product of spheres topology

@article{Schwartz2007ExistenceOO, title={Existence of outermost apparent horizons with product of spheres topology}, author={Fernando Schwartz}, journal={arXiv: General Relativity and Quantum Cosmology}, year={2007} }

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.

## 12 Citations

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