General remarks

In this chapter, we shall study a family of solutions which were constructed with the explicit aim of superposing the FLRW models with various important vacuum or electrovacuum solutions. They become the FLRW models in the homogeneous perfect fluid limit, and they reduce to the Kerr or related solutions in the stationary (electro-) vacuum limit. They were guessed rather than derived by integration of the Einstein equations. The null radiation in them was not introduced as an additional physical component of matter, but appeared ex post as a device to interpret those components of the Einstein tensor that do not belong to the perfect fluid or electromagnetic field. As a result, the various components of the source (the fluid, the electromagnetic field and the null radiation) are coupled through the parameters and functions that they all contain, and cannot be set to zero separately. Usually, setting the null radiation component to zero results in trivializing the other components automatically (for example, it may result in reducing the solution to a FLRW model or to a vacuum). This is a disadvantage, of course, but otherwise the solutions constitute a very interesting experiment in combining different models that has already reached remarkable sophistication and provided new insights into the properties of known solutions. The papers from this family do not contain sufficient information to assign the solutions to the Wainwright (1979 and 1981) classes. The solutions are displayed in Figure 5.1.