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

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

1996-09-24

arxiv.org/abs/gr-qc/9609057v1

Phys.Rev. D55 (1997) 1977-1984

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

REVTEX, 16 pages, 1 figure

Scientific paper

10.1103/PhysRevD.55.1977

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 $\Sigma$ contained within a finite topologically spherical boundary $B = \partial \Sigma$. 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.

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