  The status of canonical reduction for metric and tetrad gravity in
space-times of the Christodoulou-Klainermann type, where the ADM energy rules
the time evolution, is reviewed. Since in these space-times there is an
asymptotic Minkowski metric at spatial infinity, it is possible to define a
Hamiltonian linearization in a completely fixed (non harmonic) 3-orthogonal
gauge without introducing a background metric. Post-Minkowskian
background-independent gravitational waves are obtained as solutions of the
linearized Hamilton equations.
