ar X iv : g r - qc / 9 90 90 25 v 1 7 S ep 1 99 9 Tetrad Gravity : III ) Asymptotic Poincaré Charges , the Physical

After a review on asymptotic flatness, a general discussion of asymptotic weak and strong Poincaré charges in metric gravity is given with special emphasis on the boundary conditions needed to define the proper Hamiltonian gauge transformations and to get a differentiable Dirac Hamiltonian. Lapse and shift functions are parametrized in a way which allows to identify their asymptotic parts with the lapse and shift functions of Minkowski spacelike hyperplanes. After having added the strong (surface integrals) Poincaré charges to the Dirac Hamiltonian, it becomes the sum of a differentiable Hamiltonian and of the weak (volume integrals) Poincaré charges. By adding the ten Dirac extra variables at spatial infinity, which identify special families of foliations with leaves asymptotic (in a direction-independent way) to Minkowski spacelike hyperplanes, metric gravity is extended to englobe Dirac’s ten extra first class constraints which identify the weak Poincaré charges with the momenta conjugate to the extra variables. This opens the path to a consistent deparametrization of general relativity to parametrized Minkowski theories restricted to spacelike hyperplanes. The requirement of absence of supertranslations restricts: i) the boundary conditions on the fields and the gauge transformations to those identifying the family of Christodoulou-Klainermann spacetimes; ii) the allowed 3+1 splittings of spacetime to those whose spacelike leaves correspond to the Wigner hyperplanes of Minkowski parametrized theories [on these leaves, named Wigner-Sen-Witten hypersurfaces, there is