 
Summary: ASYMPTOTICALLY SIMPLE SOLUTIONS OF THE
VACUUM EINSTEIN EQUATIONS IN EVEN
DIMENSIONS
MICHAEL T. ANDERSON AND PIOTR T. CHRU SCIEL
Abstract. We show that a set of conformally invariant equations
derived from the FeermanGraham tensor can be used to construct
global solutions of vacuum Einstein equations, in all even dimen
sions. 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.
1. Introduction
Consider the class of vacuum solutions to the Einstein equations
(M ; g) in n + 1 dimensions, which are future asymptotically simple,
i.e. conformally compact, in the sense of Penrose, to the future of a
complete Cauchy surface (S ;
). A natural method to try to construct
such spacetimes is to solve a Cauchy problem for the compactied,
unphysical spacetime (M ;
g), and then recover the associated physical
spacetime via a conformal transformation. However, a direct approach
along these lines leads to severe diĘculties, since the conformally trans
