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
The main scope of this research consists in evaluating the energymomentum (gravitational field plus matter) and gravitational angular momentum densities in the universe with global rotation, considering the Gödel-Obukhov metric. For this, we use the Hamiltonian formalism of the Teleparallel Equivalent of General Relativity (TEGR), which is justified for presenting covariant expressions for the considered quantities. We found that the total energy density calculated by the TEGR method is in agreement with the results reported by other authors in the literature using pseudotensors. The result found for the angular momentum density depends on the rotational parameter as expected. We also show explicitly the equivalence among the field equations of the TEGR and Einstein equations (RG), considering a perfect fluid and Gödel-Obukhov metric.
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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