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  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.                
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