The theorem is often used when searching for algebraically special vacuum solutions.

We can immediately write down the general vacuum solution in Nordström's theory:

Characterization of three standard families of vacuum solutions as noted above.

Flat Minkowski space is the simplest example of a vacuum solution.

Null dusts include vacuum solutions as a special case.

The relevant vacuum solution for circular orbits is the Schwarzschild metric.

These functions specify initial data, from which a unique vacuum solution can be evolved.

For vacuum solutions, it is appropriate to use (7.8) and equations (7.9) may then be written in the form.

In this chapter we will consider only vacuum solutions.

The Geroch transformations, which relate one vacuum solution to another, in fact form an infinite-dimensional group.