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.