Energy of Isolated Systems at Retarded Times as the Null Limit of Quasilocal Energy ∗

We define the energy of a perfectly isolated system at a given retarded time as the suitable null limit of the quasilocal energy E. The result 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 Σ contained within a finite topologically spherical boundaryB = ∂Σ. Moreover, we show that with an arbitrary lapse and zero shift the same null limit of the Hamiltonian defines a physically meaningful element in the space dual to supertranslations. This result is specialized to yield an expression for the full Bondi-Sachs four-momentum in terms of Hamiltonian values. ∗Preprint numbers: NCSU/CTMP/013, TUW-10-96, IFP-730-UNC and TAR-054-UNC †Email addresses: david [email protected], [email protected], and [email protected]