Examples
In some (more or less) familiar solutions, the Weyl tensor has the same Petrov type at each event:
- the Kerr vacuum is everywhere type D,
- certain Robinson/Trautman vacuums are everywhere type III,
- the pp-wave spacetimes are everywhere type N,
- the FRW models are everywhere type O.
More generally, any spherically symmetric spacetime must be of type D (or O). All algebraically special spacetimes having various types of stress-energy tensor are known, for example, all the type D vacuum solutions.
Some classes of solutions can be invariantly characterized using algebraic symmetries of the Weyl tensor: for example, the class of non-conformally flat null electrovacuum or null dust solutions admitting an expanding but nontwisting null congruence is precisely the class of Robinson/Trautmann spacetimes. These are usually type II, but include type III and type N examples.
Read more about this topic: Petrov Classification
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