  In the framework of the rest-frame instant form of tetrad gravity, where the
Hamiltonian is the weak ADM energy ${\hat E}_{ADM}$, we define a special
completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of
{\it non-harmonic} 4-coordinates, in which the independent degrees of freedom
of the gravitational field are described by two pairs of canonically conjugate
Dirac observables (DO) $r_{\bar a}(\tau ,\vec \sigma)$, $\pi_{\bar a}(\tau
,\vec \sigma)$, $\bar a = 1,2$. We define a Hamiltonian linearization of the
theory, i.e. gravitational waves, {\it without introducing any background
4-metric}, by retaining only the linear terms in the DO's in the
super-hamiltonian constraint (the Lichnerowicz equation for the conformal
factor of the 3-metric) and the quadratic terms in the DO's in ${\hat
E}_{ADM}$. {\it We solve all the constraints} of the linearized theory: this
amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann
space-time. The Hamilton equations imply the wave equation for the DO's
$r_{\bar a}(\tau ,\vec \sigma)$, which replace the two polarizations of the TT
harmonic gauge, and that {\it linearized Einstein's equations are satisfied} .
Finally we study the geodesic equation, both for time-like and null geodesics,
and the geodesic deviation equation.
