On a Class of Riemann-Cartan Space-times of Gödel Type

Abstract

A class of Riemann-Cartan Gödel-type space-times is examined by using the equivalence problem techniques, as formulated by Fonseca-Neto et al. and embodied in a suite of computer algebra programs called TCLASSI. A coordinate-invariant description of the gravitational field for this class of space-times is presented. It is also shown that these space-times can admit a group $G_r$ of affine-isometric motions of dimensions $r=2,4,5$. The necessary and sufficient conditions for space-time (ST) homogeneity of this class of space-times are derived, extending previous works on Gödel-type space-times. The equivalence of space-times in the ST homogeneous subclass is studied, recovering recent results under different premises. The results of the limiting Riemannian case are also recovered.

21 pages, LaTex files, to appear in Gen. Rel. Grav. (1998)

References in corpus (2)

• Riemann-Cartan Space-times of Gödel Type
• Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups, Part 3: All Killing fields linearly independent of u^α and w^α

Cited by in corpus (8)

• Gödel-type universes in f(R) gravity
• Dynamics and stability of the Godel universe
• Fermions in Gödel-type background space-times with torsion and the Landau quantization
• Godel-type Universes in String-inspired Charged Gravity
• Gödel-type universes and chronology protection in Horava-Lifshitz gravity
• Gödel-type Spacetimes in Induced Matter Gravity Theory
• Riemann-Cartan Space-times of Gödel Type
• Weyl fermions in a family of Gödel-type geometries with a topological defect