The angular momentum of the gravitational field and the Poincaré group

A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space-time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow us to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincaré group.

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“…and the total angular momentum of the gravitational field, contained within a volume V of the threedimensional space, according to [51,54] …”

Section: Gravitational Angular Momentummentioning

confidence: 99%

The teleparallel equivalent of general relativity

2013

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“…The quantities P a and L ab are separately invariant under general coordinate transformations of the three-dimensional space and under time reparametrizations, which is an expected feature since these definitions arise in the Hamiltonian formulation of the theory. Moreover, these quantities transform covariantly under global SO(3, 1) transformations [39].…”

Section: The Tegr For Gravitation Energy Momentum Angular-momentummentioning

confidence: 99%

Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors, energy, momentum and angular momentum

Nashed¹

2010

Chinese Phys. B

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The energy-momentum tensor, which is coordinate independent, is used to calculate energy, momentum and angular-momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space-time their energies are different. Therefore, a regularized expression of the gravitational energy-momentum tensor of the teleparallel equivalent of general relativity, (TEGR), is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy-momentum is used to investigate the energy within the external event horizon. The components of angular-momentum associated with these space-times are calculated. In spite that we use a static space-times, we get a non-zero component of angular-momentum! Therefore, we derive the killing vectors associated with these space-times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear.Keywords: Teleparallel equivalent of general relativity, Brane world black holes, Gravitational energy-momentum tensor, Regularized expression of the gravitational energy-momentum.

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“…It is possible to simplify the constraints into a single constraint Γ ab . It is then simple to verify that the Hamiltonian density (8) may be written in the equivalent form [21] H = e a0 C a + 1 2 λ ab Γ ab ,…”

Section: The Hamiltonian Constraints Equations As An Energy and Gmentioning

confidence: 99%

“…We also verify the consistency of the tensorial expressions of the total energy-momentum and angular momentum from the Hamiltonian formalism of the TEGR. For this, we apply the Hamiltonian formulation implemented by Maluf [21][29] to find the total energy-momentum (gravitational field plus matter) and gravitational angular momentum values in the FLRW universe. It is shown that all these quantities vanish for flat and spherical geometries.…”

Section: Introductionmentioning

confidence: 99%

Energy in an expanding universe in the teleparallel geometry

Sousa¹,

Moura²,

Pereira³

2010

Braz. J. Phys.

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The main purpose of this paper is to explicitly verify the consistency of the energy-momentum and angular momentum tensor of the gravitational field established in the Hamiltonian structure of the Teleparallel Equivalent of General Relativity (TEGR). In order to reach these objectives, we obtained the total energy and angular momentum (matter plus gravitational field) of the closed universe of the Friedmann-Lemaître-Robertson-Walker (FLRW). The result is compared with those obtained from the pseudotensors of Einstein and Landau-Lifshitz. We also applied the field equations (TEGR) in an expanding FLRW universe. Considering the stress energymomentum tensor for a perfect fluid, we found a teleparallel equivalent of Friedmann equations of General Relativity (GR).

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The angular momentum of the gravitational field and the Poincaré group

Cited by 51 publications

References 26 publications

The teleparallel equivalent of general relativity

The teleparallel equivalent of general relativity

Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors, energy, momentum and angular momentum

Energy in an expanding universe in the teleparallel geometry

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