Hamiltonian boundary term and quasilocal energy flux

Chiang Mei Chen, James M. Nester, Roh Suan Tung

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Abstract

The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant.

Original languageEnglish
Article number104020
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume72
Issue number10
DOIs
StatePublished - 15 Nov 2005

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