Existence of outermost apparent horizons with product of spheres topology

Details Existence of outermost apparent horizons with product of spheres topology Existence of outermost apparent horizons with product of spheres topology

2007-04-18

arxiv.org/abs/0704.2403v2

Commun. Anal. Geom.16:799-817, 2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Replaced by revised version. Improvements in exposition and simpler proofs. 3 figures added

Scientific paper

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.

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