 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  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 &#8805; 1, we construct
   asymptotically flat, scalar flat Riemannian manifolds with smooth outermost
              apparent horizon which is, topologically, Sn  Sm+1.