SYMMETRIES OF THE STEPHANI UNIVERSES

Two classes of solutions fbr conformally flat perfect fluids exist dep ending on whether the fluid expansion vanishes or not. The expanding s olutions have become known as the Stephani universes and are generaliz ations of the well known Friedmann-Robertson-Walker solutions; the sol utions with zero expansion generalize the interior Schwarzschild solut ion. The isometry structure of the expansion-free solutions was comple tely analysed some time ago. For the Stephani universes it is shown th at any Killing vector is orthogonal to the fluid how and so the situat ion for the expanding case is somewhat simpler than the expansion-free case where 'tilted' Killing vectors may exist. The existence of isome tries in Stephani universes depends on the dimension r of the linear s pace spanned by certain functions of time a(t), b(t), c(1)(t), c(2)(t) and c(3)(t) which appear in the metric. If r is 4 or 5, no Killing ve ctors exist. If r = 3, the isometry group is one dimensional. If r = 2 , the spacetime admits a complete three-dimensional isometry group wit h two-dimensional orbits. If r = 1, there are six Killing vectors and the spacetime is Friedmann-Robertson-Walker. Mot all choices of the me tric functions a(t), b(t), c(1)(t), c(2)(t) and c(3)(t) lead to distin ct spacetimes: the ten-dimensional conformal group, which acts on each of the hypersurfaces orthogonal to the fluid flow,. preserves the ove rall form of the metric, but induces a group of transformations on the se five metric functions which is locally isomorphic to SO(4, 1). A re sult of the same ilk is derived for the non-expanding solutions.