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

J. D. Brown·S. R. Lau·J. W. York, Jr
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Abstract

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 boundary $B = \partial Σ$. 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.

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J. D. Brown, S. R. Lau, J. W. York, Jr. 1996-09-24. Energy of Isolated Systems at Retarded Times as the Null Limit of Quasilocal Energy. https://doi.org/10.1103/physrevd.55.1977

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