Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

We analyse type I vacuum solutions admitting an isometry whose Killing 2-form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group G3 of isometries. We give a classification of this family and study the Bianchi type for each class. The classes compatible with an aligned Killing 2-form are also determined. The Szekeres–Brans theorem is extended to non-vacuum spacetimes with vanishing Cotton tensor.