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Fernando Schwartz : On the topology of black holes

An important special case of the general construction of black holes translates into a problem in Riemannian geometry, since a totally geodesic slice of spacetime is an asymptotically flat Riemannian manifold with nonnegative scalar curvature, and the restriction of the event horizon to the slice is the apparent horizon in the slice. In this talk we show how to construct new examples of Riemannian manifolds with nonspherical apparent horizon, in dimensions four and above. More precisely, for any $n,m\ge 1$, we construct asymptotically flat, scalar flat Riemannian manifolds with apparent horizon that is a smooth outermost minimal hypersurface with topology $S^n\times S^{m+1}$.

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