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

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