Energy and Momentum in Spacetime Homogeneous G$\ddot{o}$del-type Metrics

TL;DR

This paper calculates energy and momentum distributions in G"odel-type spacetimes using Einstein and Papapetrou complexes, revealing discrepancies between the two methods but aligning with existing G"odel metric results.

Contribution

It compares two energy-momentum complexes in G"odel-type metrics and shows their results differ, yet both agree with known G"odel metric energy-momentum densities.

Findings

Einstein and Papapetrou complexes yield different energy-momentum distributions.

Results reduce to known G"odel metric energy-momentum densities.

Discrepancies highlight complexities in defining energy-momentum in such spacetimes.

Abstract

Using Einstein and Papapetrou energy-momentum complexes, we explicitly calculate the energy and momentum distribution associated with spacetime homogeneous G$\ddot{o}$del-type metrics. We obtain that the two definitions of energy-momentum complexes do not provide the same result for these type of metrics. However, it is shown that the results obtained are reduced to the energy-momentum densities of G$\ddot{o}$del metric already available in the literature