Energy and angular momentum densities in a Gödel-type universe in teleparallel geometry

A.A. Sousa, R.B. Pereira and A.C. Silva1

Abstract

The main scope of this research consists in evaluating the energy-momentum (gravitational field plus matter) and gravitational angular momentum densities in the universe with global rotation, considering the Gödel-Obukhov metric. To do that, we use the Hamiltonian formalism of the Teleparallel equivalent of general relativity (TEGR), which is justified for presenting covariant expressions for the quantities under consideration. We have 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 the Einstein equations (GR), considering a perfect fluid and the Gödel-Obukhov metric.

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