ISOMETRIC EMBEDDING OF THE SPHERICALLY SYMMETRICAL STEPHANI UNIVERSE - SOME EXPLICIT EXAMPLES

Some general properties of the local isometric embedding of the spherically symmetric Stephani universe are examined. A representative set of the explicit embeddings is found. It is composed of the embeddings of the Stephani-de Sitter universe (the de Sitter universe with unusual foliation) and the embeddings of the really inhomogeneous (though still spherically symmetric) Stephani universe. In order to investigate the structure of infinity and the light propagation in space-time each embedding is accompanied by a suitable Penrose diagram. It is realized that apart from both the density and pressure big-bang-type singularities, also the finite-density singularities of pressure appear in the model. The latter singularities are carefully discussed because they exist in the general, not even spherically symmetric Stephani universe. Under some conditions these singularities can be avoided.