  A discussion of asymptotic weak and strong Poincare' charges in metric
gravity is given to identify the proper Hamiltonian boundary conditions. The
asymptotic part of the lapse and shift functions is put equal to their
analogues on Minkowski hyperplanes. By adding Dirac's ten extra variables at
spatial infinity, metric gravity is extended to incorporate Dirac's ten extra
first class constraints (the new ten momenta equal to the weak Poincare'
charges) and this allows its deparametrization to parametrized Minkowski
theories restricted to spacelike hyperplanes. The absence of supertranslations
implies: i) boundary conditions identifying the family of
Christodoulou-Klainermann spacetimes; ii) the restriction of foliations to
those (Wigner-Sen-Witten hypersurfaces) corresponding to Wigner's hyperplanes
of Minkowski rest-frame instant form. These results are generalized to tetrad
gravity in the new formulation given in gr-qc/9807072, gr-qc/9807073. The
evolution in the parameter labelling the leaves of the foliation is generated
by the weak ADM energy. Some comments on the quantization in a completely fixed
special 3-orthogonal gauge are made.
