Constant scalar curvature hypersurfaces in extended Schwarzschild   space-time
  We present a class of spherically symmetric hypersurfaces in the   Kruskal extension of the Schwarzschild space-time. The hypersurfaces have constant negative scalar curvature, so they are hyperboloidal in the regions of space-time which are asymptotically flat. 
M. J. Pareja and J. Frauendiener