Homogeneity of Riemannian space-times of Goedel type
The conditions for space-time homogeneity of a Riemannian manifold with a Goedel-type metric are examined. The Raychaudhuri-Thakurta necessary conditions for space-time homogeneity are shown to be also sufficient and to lead to five linearly independent Killing vectors. These vector fields are exhibited for the most general case and their algebra is examined. The irreducible set of isometrically independent space-time--homogeneous Goedel- p type metrics is shown to be given, in cylindrical coordinates, by ds/sup 2/ = (dt+(4..cap omega../m/sup 2/)sinh/sup 2/(mr r/2)dphi)/sup 2/-(1/m/sup 2/)sinh/sup 2/(mr )dphi/sup 2/-dr/sup 2/-dz/sup 2/, where ..cap omega.. is the vorticity and -infinity< or =m/sup 2/< or =+infinity, m/sup 2/ = 2..cap omega../sup 2/ corresponding to the Goedel metric. Sources of Einstein's equations leading to these metrics as solutions are examined, and it is shown that the inclusion of a scalar field extends the previously known region of solutions -infinity< or =m/sup 2/< or =2..cap omega../sup 2/ to -infinity< or =m/sup 2/< or =4..cap omega../sup 2/. The problem of ambiguity of physical sources of the same metric and that of violation of causality in Goedel-type space-time--homogeneous universes are examined. In the case m/sup 2/ = 4..cap omega../sup 2/, we obtain the first exact Goedel-type solution of Einstein's equations describing a completely causal space-time--homogeneous rotating universe.
- Research Organization:
- Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150-Urca, 22.290-Rio de Janeiro, RJ, Brasil
- OSTI ID:
- 5810670
- Journal Information:
- Phys. Rev. D; (United States), Vol. 28:6
- Country of Publication:
- United States
- Language:
- English
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