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\textsc{Analysis and Differential Geometry}
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\textsc{Seminar}
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\textit{On the topology of black holes}
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Fernando Schwartz\par
Duke University
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\textbf{Abstract:} Interest in constructing new examples of high dimensional black
hole spacetimes has increased recently, mostly due to string theory.
Despite the fact that event horizons need not be spherical in dimensions
greater than four, only one class of examples of nonspherical black
holes is known to exist, and it is specific to dimension five -- the so-called
rotating black rings with horizon topology S1 x S2.

An important special case in the construction of spacetimes translates
into a problem in Riemannian geometry. Indeed, asymptotically
flat Riemannian manifolds with nonnegative scalar curvature are totally
geodesic slices of spacetime, and the resctriction of the event
horizon to the slice is the outermost apparent horizon in the slice.
In this talk we show how to construct slices that have ring apparent
horizon. More precisely, for any n,m at least 1, we construct asymptotically
flat, scalar flat Riemannian manifolds with smooth outermost apparent
horizon which is, topologically, Sn x Sm+1.\vspace{\fill}
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Tuesday, September 25, 2007, 4:00 pm\par
Mathematics and Science Center: W301
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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