Role of shear in general-relativistic cosmological and stellar models

We investigate the class of shear-free expanding (or contracting) irrotational perfect fluids obeying an equation of state $p=p\left(\mu \right)$ and satisfying the field equations of general relativity. It is shown that these space-times are either Friedmann-Robertson-Walker, or spherically symmetric Wyman solutions, or a special class of plane-symmetric models. This last class, which is given in exact form, is apparently new; the metrics are locally either spatially or temporally homogeneous. We show that the spherically symmetric Wyman solutions and the new class of plane-symmetric models are inconsistent with the additional requirement of a comoving surface of zero pressure, and thereby obtain a coordinate-free proof and a generalization of a result of Mansouri, concerning shear-free spherically symmetric gravitational collapse. Some properties of our solutions, and further generalizations of our results, are considered.