Inhomogeneous cosmological models which are homogeneous and isotropic on average

A scheme to construct inhomogeneous universes which are nevertheless homogeneous and isotropic on average is presented in the framework of general relativity for models containing dust and a cosmological constant. A class of exact solutions is shown in the case that the collapse is locally one dimensional. They represent "relativistic pancake solutions" analogous to Zel'dovich's solution in Newtonian cosmology. The relation to gauge-invariant perturbation theory is also discussed.