Energy-momentum and angular momentum of Goedel universes

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 Gödel models.

arXiv commentan amended version, 24 pages, accepted to PRD

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• Gödel-type universes and chronology protection in Horava-Lifshitz gravity
• Violation of causality in $f(T)$ gravity
• Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity
• Energy and Angular Momentum Densities in a Godel-Type Universe in the Teleparallel Geometry
• Observing other universe through ringholes and Klein-bottle holes