By G. Ellis, H. van Elst

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These will be discussed after briefly considering observations. 23 This kind of change happens also in the maximally extended Schwarzschild solution at the event horizon. 3 50 Observational relations Observational relations in these universes have been examined in detail. (a) Redshift, area distance, and galaxy observations ((M, z) and (N, z) relations) are considered in MacCallum and Ellis [128]. Anisotropies can occur in all these relations, but many of the models will display discrete isotropies in the sky.

G. fixed points). Consequently, the dimension of the orbits through special points is lower than that of orbits through general points. The dimension of the orbit and isotropy group is the same at each point of an orbit, because of the equivalence of the group action at all points on each orbit. The group is transitive on a surface S (of whatever dimension) if it can move any point of S into any other point of S. Orbits are the largest surfaces through each point on which the group is transitive; they are therefore sometimes referred to as surfaces of transitivity.

Exercise: Show how appropriate choice of initial data in a LTB model can give an effective SwissCheese model with one centre surrounded by a series of successive FLRW and non-FLRW spherical regions. Can you include (i) flat, (ii) vacuum (Schwarzschild) regions in this construction? One of the most intriguing questions is what non-spherically symmetric models can be joined regularly onto a FLRW model. Bonnor has shown that some Szekeres anisotropic and inhomogeneous models can be matched to a dust FLRW model across a comoving spherical junction surface [167].