Energy-momentum and angular momentum of Gödel universes

We discuss the Einstein energy-momentum complex and the Bergmann-Thomson angular momentum complex in general relativity and calculate them for space-time homogeneous Gödel universes. The calculations are performed for a dust acausal Gödel model and for a scalar-field causal Gödel model. It is shown that the Einstein pseudotensor is traceless, not symmetric, the gravitational energy “density” is negative, and that the gravitational Poynting vector vanishes. Significantly, the total (gravitational and matter) energy “density” for the acausal model is zero while for the causal model it is negative. The Bergmann-Thomson angular momentum complex does not vanish for both Gödel models.