On the homogeneity of Riemannian space-times of Goedel type

The conditions for space-time homogeneity of a Riemannian manifold with a Godel-type metric are examined. The Raychaudhuri-Thakurta necessary conditions 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 are examined. The irreducible set of isometrically independent ST-homogeneous Godel-type metrics is shown to be given, in cylindrical coordinates, by ds2 = [dt + 4Ω/m2 sinh2 (mr)/2) d phi]2 - 1/m2 sinh2 (mr) d phi2 - dr2 - dz2, where Ω is the vorticity and - infinity < = m2 < = + infinity, m2 = 2Ω2 corresponding to the Godel metric. Sources of Einstein 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 < = m2 < = 2Ω2 to - infinity < = m2 < = 4Ω2. The problem of ambiguity of physical sources of the same metric and that of violation of causality in Godel-type ST-homogeneous universes are examined. In the case m2 = 4Ω2 the first exact Godel-type solution of Einstein equations describing a completely causal ST-homogeneous rotating universe is obtained. (Author)