Superenergy and Supermomentum of Goedel Universes

Abstract

We review the canonical superenergy tensor and the canonical angular supermomentum tensors in general relativity and calculate them for space-time homogeneous Gödel universes to show that both of these tensors do not, in general, vanish. We consider both an original dust-filled pressureless acausal Gödel model of 1949 and a scalar-field-filled causal Gödel 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 Gödel 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.

an amended version, REVTEX, 26 pages, no figures, to appear in Classical and Quantum Gravity

References in corpus (3)

• Super-energy tensors
• Gödel-type Spacetimes in Induced Matter Gravity Theory
• Super-energy tensor for space-times with vanishing scalar curvature

Cited by in corpus (9)

• Fermions in Gödel-type background space-times with torsion and the Landau quantization
• The Gödel solution in the modified gravity
• Weyl fermions in a family of Gödel-type geometries with a topological defect
• Moeller's Energy-Momentum Complex for a Spacetime Geometry on a Noncommutative Curved D3-Brane
• Massless field perturbations of the spinning C metric
• Vorticity survival in magnetised Friedmann universes
• Energy-momentum and angular momentum of Goedel universes
• Statefinders and observational measurement of superenergy
• The averaged tensors of the relative energy-momentum and angular momentum in general relativity and some their applications