Energy-momentum and angular momentum of Goedel universes

TL;DR

This paper calculates energy-momentum and angular momentum complexes in G"odel universes within general relativity, revealing differences between causal and acausal models in their energy densities and angular momentum properties.

Contribution

It provides the first detailed calculations of Einstein and Bergmann-Thomson complexes for G"odel universes, comparing causal and acausal models.

Findings

Einstein pseudotensor is traceless and not symmetric.

Gravitational energy density is negative; Poynting vector vanishes.

Total energy density is zero for acausal and negative for causal G"odel models.

Abstract

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