Energy and Momentum densities of cosmological models, with equation of state $\rho=\mu$, in general relativity and teleparallel gravity

TL;DR

This paper computes energy and momentum densities for stiff fluid cosmological models using various complexes in both general relativity and teleparallel gravity, revealing their differences and similarities.

Contribution

It compares energy-momentum complexes in general relativity and teleparallel gravity for stiff fluid models, highlighting their equivalence and differences.

Findings

Different complexes yield different energy-momentum densities within the same theory.

Each complex's results are consistent across both theories.

Axial-vector torsion vanishes for the studied spacetime.

Abstract

We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex's value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.