Homogeneous space-times of the Gödel type

The condition for homogeneity of a class of cylindrically symmetric metrics is investigated. This leads to the discovery of a general solution from which a number of metrics (obtained earlier by different authors, including the two forms of the Gödel metric) are recovered by choosing the integration constants suitably. Incidentally, it is found that the same electromagnetic stress-energy tensor admits alternative interpretations as a Maxwell field either without sources or with a continuous distribution of sources.