Gravito-magnetic vacuum spacetimes: kinematic restrictions

TL;DR

This paper proves that vacuum spacetimes with purely magnetic Weyl tensors cannot exist under certain kinematic restrictions, extending previous results and using a covariant approach based on Bianchi identities.

Contribution

It generalizes prior non-existence results to include cases with specific kinematic restrictions and applies a covariant method that also covers non-vacuum solutions with vanishing Cotton tensor.

Findings

No vacuum solutions with purely magnetic Weyl tensor under the specified kinematic conditions.

Results are valid for non-vacuum solutions with vanishing Cotton tensor.

Uses a covariant approach emphasizing Bianchi identities.

Abstract

We show that there are no vacuum solutions with a purely magnetic Weyl tensor with respect to an observer submitted to kinematic restrictions involving first order differential scalars. This result generalizes previous ones for the vorticity-free and shear-free cases. We use a covariant approach which makes evident that only the Bianchi identities are used and, consequently, the results are also valid for non vacuum solutions with vanishing Cotton tensor.