ENERGY OF ISOLATED SYSTEMS AT RETARDED TIMES AS THE NULL LIMIT OF QUASI-LOCAL ENERGY

We define the energy of a perfectly isolated system at a given retarde d time as the suitable null limit of the quasilocal energy E. The resu lt coincides with the Bondi-Sachs mass. Our E is the lapse-unity shift -zero boundary value of the gravitational Hamiltonian appropriate for the partial system Sigma contained within a finite topologically spher ical boundary B = partial derivative Sigma. Moreover, we show that wit h an arbitrary lapse and zero shift the same null limit of the Hamilto nian defines a physically meaningful element in the space dual to supe rtranslations. This result is specialized to yield an expression for t he full Bondi-Sachs four-momentum in terms of Hamiltonian values.