Canonical Formulation of Gravitational Teleparallelism in 2+1 Dimensions in Schwinger's Time Gauge

Sousa, A. A.; Maluf, J. W.

doi:10.1143/ptp.104.531

Cited by 17 publications

(23 citation statements)

References 11 publications

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“…Let us verify the consistency of the expression of gravitational angular momentum (18). By making use of (19) and (17) we can write (18) in the form…”

Section: Gravitational Angular Momentummentioning

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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“…Let us verify the consistency of the expression of gravitational angular momentum (18). By making use of (19) and (17) we can write (18) in the form…”

Section: Gravitational Angular Momentummentioning

confidence: 99%

Energy in an expanding universe in the teleparallel geometry

Sousa¹,

Moura²,

Pereira³

2010

Braz. J. Phys.

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“…12) The crucial point in this analysis is that only the symmetrical components p (ij) depend on the "velocities" ∆ a0k . The other three components, p [ij] and p 0k depend solely on T aij .…”

Section: Conditions On the Free Parametersmentioning

confidence: 99%

“…It turns out, however, that consistent values for the gravitational angular momentum are achieved by requiring the triad field to satisfy (a posteriori) the time gauge condition (this seems to be a requirement to obtain the irreducible mass of the Kerr black hole, in the four-dimensional case). 10) In the region near to the surface of the BTZ black hole r > r 0 , we arrive at M 12 …”

Section: §1 Introductionmentioning

confidence: 99%

Angular Momentum of the BTZ Black Hole in the Teleparallel Geometry

Sousa¹,

Pereira²,

Rocha-Neto³

2005

Progress of Theoretical Physics

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We carry out the Hamiltonian formulation of the three- dimensional gravitational teleparallelism without imposing the time gauge condition, by rigorously performing the Legendre transform. Definition of the gravitational angular momentum arises by suitably interpreting the integral form of the constraint equation Gama^ik=0 as an angular momentum equation. The gravitational angular momentum is evaluated for the gravitational field of a rotating BTZ black hole.Comment: 17 pages, no figures, v2: some misprints corrected, Ref.s added, Eq.s revised, submitted to General Relativity and Gravitatio

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“…However, they are conceptually quite different. In particular, the teleparallel formulation of gravity is described by a vanishing curvature and a non-vanishing torsion which characterizes the parallel transport [1][2][3][4][5]. In such case, the geometry is no more Riemannian but corresponds to the so-called Riemannian-Cartan (Weizenböck) geometry.…”

Section: Introductionmentioning

confidence: 99%

“…(A.3)The field equations of the CS supergravity theory based on the AdS superalgebra are given by the vanishing of the super-AdS curvature two-forms, namelỹR a = R a + 1 2 γ a ψ = 0 , T a = T a + 1 2ψ γ a ψ = 0 , = dψ + 1 2 ω a γ a ψ + 1 e a γ a ψ = 0 . (A 4).…”

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confidence: 99%

Three-dimensional teleparallel Chern-Simons supergravity theory

et al. 2021

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In this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincaré algebra. At the bosonic level the theory describes a non-Riemannian geometry with a non-vanishing torsion. In presence of supersymmetry, the teleparallel supergravity theory is characterized by a non-vanishing super-torsion in which the cosmological constant can be seen as a source for the torsion. We show that the teleparallel supergravity theory presented here reproduces the Poincaré supergravity in the vanishing cosmological limit. The extension of our results to $${\mathcal {N}}=p+q$$ N = p + q supersymmetries is also explored.

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Canonical Formulation of Gravitational Teleparallelism in 2+1 Dimensions in Schwinger's Time Gauge

Cited by 17 publications

References 11 publications

Energy in an expanding universe in the teleparallel geometry

Energy in an expanding universe in the teleparallel geometry

Angular Momentum of the BTZ Black Hole in the Teleparallel Geometry

Three-dimensional teleparallel Chern-Simons supergravity theory

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