Type I vacuum solutions with aligned Papapetrou fields: an intrinsic characterization

Abstract

We show that Petrov type I vacuum solutions admitting a Killing vector whose Papapetrou field is aligned with a principal bivector of the Weyl tensor are the Kasner and Taub metrics, their counterpart with timelike orbits and their associated windmill-like solutions, as well as the Petrov homogeneous vacuum solution. We recover all these metrics by using an integration method based on an invariant classification which allows us to characterize every solution. In this way we obtain an intrinsic and explicit algorithm to identify them.

14 pages; v2: added new section, references and table

References in corpus (2)

• On the classification of type D spacetimes
• Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

Cited by in corpus (5)

• 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
• Particle Dynamics on Test Papapetrou Fields of Vacuum Spacetimes
• Dimension of the isometry group in spacetimes with an invariant frame