Canonical Reduction of Gravity: from General Covariance to Dirac Observables and post-Minkowskian Background-Independent Gravitational Waves

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.