Develop Galilean analogues of relativistic Weyl-tensor applications

Develop non-relativistic analogues of the Petrov classification of spacetimes and investigate whether the Galilean Weyl tensor can be used to understand non-relativistic gravitational radiation.

Background

The paper constructs an off-shell, conformally invariant Galilean Weyl tensor and its electric and magnetic parts. The authors suggest that these objects might support applications analogous to those of the relativistic Weyl tensor, including spacetime classification and the analysis of gravitational radiation. The proposed extensions are not developed or resolved in the paper.

References

With a fully general understanding of Galilean Weyl tensors in hand, it is natural to ask whether this object can be leveraged in ways analogous to the relativistic context---for example, in developing a non-relativistic analogue of the Petrov classification of spacetimes, or in understanding non-relativistic gravitational radiation (on which see ref.).

— An off-shell conformally invariant Galilean Weyl tensor  (2609.04053 - Vigneron et al., 3 Sep 2026) in Conclusion, final future-directions list