Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

TL;DR

This paper classifies vacuum type I spacetimes with aligned Killing 2-forms, revealing their symmetry groups and extending a theorem to certain non-vacuum cases, enhancing understanding of spacetime symmetries.

Contribution

It provides a classification of vacuum type I solutions with aligned Killing 2-forms and explores their symmetry properties, extending existing theorems to broader contexts.

Findings

Solutions admit a G_3 isometry group.

Classification of solutions based on Bianchi types.

Extension of Szekeres-Brans theorem to non-vacuum cases.

Abstract

We analyze 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 $G_3$ of isometries. We give a classification of this family and we 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.