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

TL;DR

This paper characterizes specific Petrov type I vacuum solutions admitting a special aligned Killing vector, identifying known metrics like Kasner and Taub through an invariant classification and explicit algorithm.

Contribution

It provides an intrinsic, explicit classification method to identify Petrov type I vacuum solutions with aligned Papapetrou fields, including known metrics.

Findings

Identified Kasner and Taub metrics as solutions with aligned Papapetrou fields.

Developed an invariant classification algorithm for these solutions.

Revealed a comprehensive characterization of Petrov type I vacuum solutions.

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.