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ASYMPTOTICALLY SIMPLE SOLUTIONS OF THE VACUUM EINSTEIN EQUATIONS IN EVEN
 

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 Fe erman-Graham 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 space-times is to solve a Cauchy problem for the compacti ed,
unphysical space-time (M ; 
g), and then recover the associated physical
space-time via a conformal transformation. However, a direct approach
along these lines leads to severe diĘculties, since the conformally trans-

  

Source: Anderson, Michael - Department of Mathematics, SUNY at Stony Brook

 

Collections: Mathematics