The gravitational energy–momentum flux

The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasi-local values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasi-local 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 quasi-local 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 quasi-local expressions which asymptotically give the ADM energy, the TrautmanBondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant.

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“…Note that they are significantly different in appearance from those obtained using (28) along with (17,18,21,22):…”

Section: Flux Expressionsmentioning

confidence: 56%

“…Nevertheless there still is considerable interest in this topic and some significant progress has been made recently; see in particular [13,14,15,16,17,18,19]. We include here some applications of our new natural energy flux expressions.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian boundary term and quasilocal energy flux

2005

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“…In the framework of the TEGR it has been possible to address the longstanding problem of defining the energy, momentum and angular momentum of the gravitational field [6,7,8]. The tetrad field seems to be a suitable field quantity to address this problem, because it yields the gravitational field and at the same time establishes a class of reference frames in space-time [9].…”

Section: Introductionmentioning

confidence: 99%

The angular momentum of the gravitational field and the Poincaré group

Maluf

Ulhoa

Faria

et al. 2006

Class. Quantum Grav.

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We redefine the gravitational angular momentum in the framework of the teleparallel equivalent of general relativity. In similarity to the gravitational energy-momentum, the new definition for the gravitational angular momentum is coordinate independent. By considering the Poisson brackets in the phase space of the theory, we find that the gravitational energy-momentum and angular momentum correspond to a representation of the Poincaré group. This result allows us to define Casimir type invariants for the gravitational field.

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“…There is an important issue concerning how much energy flux flows into and out of the considered region. There continues to be considerable interest this topic [10,11,12,13]. In this work we also investigate a natural expression for the energy flux associated with the aforementioned quasi-local energy [7].…”

Section: Introductionmentioning

confidence: 99%