Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-02-21
Class.Quant.Grav. 19 (2002) 1-16
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
an amended version, REVTEX, 26 pages, no figures, to appear in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/19/1/301
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.
Dabrowski Mariusz P.
Garecki Janusz
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