2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/34513A Hamiltonian linearization of the rest-frame instant form of tetrad gravity (gr-qc/0302084), where the Hamiltonian is the weak ADM energy ${\hat E}_{ADM}$, in a completely fixed (non harmonic) 3-orthogonal Hamiltonian gauge is defined. For the first time this allows to find an explicit solution of all the Hamiltonian constraints and an associated linearized solution of Einstein's equations. It corresponds to background-independent gravitational waves in a well defined post-Minkowskian Christodoulou-Klainermann space-time.RevTex4, 4 pages, 4 figuresGeneral Relativity and Quantum CosmologyAstrophysicsHigh Energy Physics - Theorytext