The aim of this work is to provide a proof of the nonlinear
gravitational stability of the Minkowski space-time. More
precisely, the book offers a constructive proof of global, smooth
solutions to the Einstein Vacuum Equations, which look, in the
large, like the Minkowski space-time. In particular, these
solutions are free of black holes and singularities. The work
contains a detailed description of the sense in which these
solutions are close to the Minkowski space-time, in all directions.
It thus provides the mathematical framework in which we can give a
rigorous derivation of the laws of gravitation proposed by Bondi.
Moreover, it establishes other important conclusions concerning the
nonlinear character of gravitational radiation. The authors obtain
their solutions as dynamic developments of all initial data sets,
which are close, in a precise manner, to the flat initial data set
corresponding to the Minkowski space-time. They thus establish the
global dynamic stability of the latter.
Originally published in 1994.
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