Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

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.

19 pages; a reference added

References in corpus (2)

• A Rainich-like approach to the Killing-Yano tensors
• Gravito-magnetic vacuum spacetimes: kinematic restrictions

Cited by in corpus (7)

• On the invariant symmetries of the $\mathcal{D}$-metrics
• Intrinsic, deductive, explicit, and algorithmic characterization of the Szekeres-Szafron solutions
• An intrinsic characterization of 2+2 warped spacetimes
• Type I vacuum solutions with aligned Papapetrou fields: an intrinsic characterization
• Particle Dynamics on Test Papapetrou Fields of Vacuum Spacetimes
• On the super-energy radiative gravitational fields
• Dimension of the isometry group in spacetimes with an invariant frame