Space-times with spherically symmetric hypersurfaces

When discussing spherically symmetric gravitational fields one usually assumes that the whole space-time is invariant under theO(3) group of transformations. In this paper, the Einstein field equations are investigated under the weaker assumption that only the 3-spacest=const areO(3) symmetric. The following further assumptions are made: (1) Thet lines are orthogonal to the spacest=const. (2) The source in the field equations in a perfect fluid, or dust, or the term, or the empty space. (3) With respect to the center of symmetry the fluid source may move only radially if at all. Under these assumptions one solution with a perfect fluid source, found previously by Stephani, is recovered and interpreted geometrically, and it is shown that it is the sole solution which is not spherically symmetric in the traditional sense. The paper ends with a general discussion of cosmological models whose 3-spacest=const are the same as in the Robertson-Walker models. No new solutions were explicitly found, but it is shown that such models exist in which the sign of curvature is not fixed in time.