A Kruskal-like model with finite density

The Novikov coordinates for the Kruskal-Schwarzschild spacetime are derived from the Tolman model (1934) and generalised. It is then shown that models with identical two-sheets-and-a-neck topologies can have a non-zero density and that other unusual topologies are possible for Tolman models. The introduction of matter into such a model is found to split the horizons in the two sheets, and to reduce communication between them. The topology of the neck always requires paired white and black holes, which in these models are the big bang and big crunch singularities. It is concluded that worm holes between universes can also exist in cosmological (i.e. dynamic, non-vacuum) models.