Energy of isolated systems at retarded times as the null limit of quasilocal energy

J. David Brown, Stephen R. Lau, and James W. York, , Jr.
Phys. Rev. D 55, 1977 – Published 15 February 1997
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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=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.

  • Received 25 September 1996

DOI:https://doi.org/10.1103/PhysRevD.55.1977

©1997 American Physical Society

Authors & Affiliations

J. David Brown

  • Department of Physics and Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8202

Stephen R. Lau

  • Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Österreich, Germany

James W. York, , Jr.

  • Institute of Field Physics and Theoretical Astrophysics and Relativity Group, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina, 27599-3255

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Issue

Vol. 55, Iss. 4 — 15 February 1997

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