Superenergy and Supermomentum of Goedel Universes

TL;DR

This paper reviews superenergy and supermomentum tensors in general relativity, calculating them for G"odel universes to explore their relation to causality and rotation, revealing non-vanishing values and potential causality indicators.

Contribution

It provides the first detailed calculation of superenergy and supermomentum tensors for G"odel universes, highlighting their sensitivity to causality and rotation in cosmological models.

Findings

Superenergy tensors do not vanish in G"odel universes.

Superenergy density differs between causal and acausal models.

Superenergetic quantities may indicate causality in cosmology.

Abstract

We review the canonical superenergy tensor and the canonical angular supermomentum tensors in general relativity and calculate them for space-time homogeneous G\"odel universes to show that both of these tensors do not, in general, vanish. We consider both an original dust-filled pressureless acausal G\"odel model of 1949 and a scalar-field-filled causal G\"odel model of Rebou\c cas and Tiomno. For the acausal model, the non-vanishing components of superenergy of matter are different from those of gravitation. The angular supermomentum tensors of matter and gravitation do not vanish either which simply reflects the fact that G\"odel universe rotates. However, the axial (totally antisymmetric) and vectorial parts of supermomentum tensors vanish. It is interesting that superenergetic quantities are {\it sensitive} to causality in a way that superenergy density $_g S_{00}$ of gravitation in the acausal model is {\it positive}, while superenergy density $_g S_{00}$ in the causal model is {\it negative}. That means superenergetic quantities might serve as criterion of causality in cosmology and prove useful.