Energy and Angular Momentum Densities in a Godel-Type Universe in the Teleparallel Geometry

TL;DR

This paper evaluates energy-momentum and angular momentum densities in a rotating Godel-type universe using the Teleparallel Equivalent of General Relativity, confirming consistency with existing results and exploring rotational effects.

Contribution

It applies the TEGR Hamiltonian formalism to compute energy and angular momentum densities in a Godel-Obukhov universe, demonstrating their dependence on rotation and confirming theoretical equivalence.

Findings

Total energy density agrees with previous pseudotensor results

Angular momentum density depends on the rotational parameter

Field equations of TEGR are equivalent to Einstein equations

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 Godel-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 Godel-Obukhov metric.