Quasilocal energy-momentum and energy flux at null infinity

Wu, Xiao-Ning; Chen, Chiang-Mei; Nester, James M.

doi:10.1103/physrevd.71.124010

Cited by 5 publications

(8 citation statements)

References 25 publications

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“…This seeming calamity is actually providential-it is directing us to additional physics contained within the formalism, namely energy flux expressions. 25,85,151 v Sufficient, but not necessary. When examined in detail it can be seen that one really only needs conditions on certain combinations of the components, but it is not in the spirit of our treatment to break fields up into, e.g., components parallel to and perpendicular to some specific boundary surface, etc.…”

Section: Null Infinitymentioning

confidence: 99%

Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach

Chen

Nester

Tung

2017

One Hundred Years of General Relativity

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Our topic concerns a long standing puzzle: the energy of gravitating systems. More precisely we want to consider, for gravitating systems, how to best describe energy-momentum and angular momentum/center-of-mass momentum (CoMM). It is known that these quantities cannot be given by a local density. The modern understanding is that (i) they are quasi-local (associated with a closed 2-surface), (ii) they have no unique formula, (iii) they have no reference frame independent description. In the first part of this work we review some early history, much of it not so well known, on the subject of gravitational energy in Einstein's general relativity (GR), noting especially Noether's contribution. In the second part we review (including some new results) much of our covariant Hamiltonian formalism and apply it to Poincaré gauge theories of gravity (PG), with GR as a special case. The key point is that the Hamiltonian boundary term has two roles, it determines the quasi-local quantities, and, furthermore it determines the boundary conditions for the dynamical variables. Energy-momentum and angular momentum/CoMM are associated with the geometric symmetries under Poincaré transformations. They are best described in a local Poincaré gauge theory. The type of spacetime that naturally has this symmetry is Riemann-Cartan spacetime, with a metric compatible connection having, in general, both curvature and torsion. Thus our expression for the energy-momentum of physical systems is obtained via our covariant Hamiltonian formulation applied to the PG. d One reason was his famous "hole" argument. 61,98 e Einstein and Hilbert had quite different agendas; 112,115,136,141 Hilbert in his Foundation of Physics papers, based on the work of Einstein and Mie, was using his axiomatic method with the objective of finding a unified field theory of gravity and electromagnetism. 15,28,58,108,109,114 July 28, 2015 0:26 World Scientific Review Volume -9.75in x 6.5in 100GR˙Ch4˙150726v1 page 5Gravitational energy for GR and Poincaré gauge theories:a covariant Hamiltonian approach 5 l The sign in this expression is dictated by the condition for positive energy determined by the Hamiltonian using our local Minkowski signature convention: Pµ = (−E/c, p).

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Section: Null Infinitymentioning

confidence: 99%

Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach

Chen

Nester

Tung

2017

One Hundred Years of General Relativity

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“…(11.5), are calculated in [563]. It is shown that, with Minkowski spacetime as a reference configuration, and even with three different embeddings of the two-surface into the reference spacetime, the null infinity limit of these two quantities are just the standard Bondi energy and Bondi mass-loss, respectively.…”

Section: Towards a Full Hamiltonian Approachmentioning

confidence: 99%

Quasi-Local Energy-Momentum and Angular Momentum in General Relativity

Szabados

2009

Living Rev. Relativ.

329

390

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The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned.

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“…With the asymptotics (25,26) it is straightforward to verify, as we just stated, that all four of our Hamiltonians are differentiable on the specified phase space-since all the boundary terms in the variations of the Hamiltonians vanish asymptotically; moreover the quasi-local expressions all give the same (since they differ by terms of the form N ∆ϕ∆p which vanish asymptotically) finite constant values (independent of the perturbation α Note that the indicated asymptotic behavior is sufficient but hardly necessary. In practice only the specific projected component combinations that actually show up in the boundary integrand need be so restricted (moreover one need only require this behavior up to a closed form).…”

Section: The Phase Space and Asymptoticsmentioning

confidence: 99%

“…We have reexpressed (57,66) in the asymptotically null regime using the NP spin coefficient formalism and obtained good results [26]. Moreover we are presently working on adapting our expressions to conformal infinity; the results of that investigation will be reported in due course.…”

Section: Application To Einstein's Gravity Theorymentioning

confidence: 99%

Hamiltonian boundary term and quasilocal energy flux

2005

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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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Quasilocal energy-momentum and energy flux at null infinity

Cited by 5 publications

References 25 publications

Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach

Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach

Quasi-Local Energy-Momentum and Angular Momentum in General Relativity

Hamiltonian boundary term and quasilocal energy flux

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