Asymptotically simple solutions of the vacuum Einstein equations in even   dimensions
  We show that a set of conformally invariant equations derived from the Fefferman-Graham tensor can be used to construct global solutions of the vacuum Einstein equations, in all even dimensions. This gives, in particular, a new, simple proof of Friedrich's result on the future hyperboloidal stability of Minkowski space-time, and extends its validity to even dimensions. 
Michael T. Anderson and Piotr T. Chrusciel