*Cosmo Comments*. The following comments can also be viewed as annotations on the paper via Hypothesis.

This is an excellent article, rigorous and clearly written, which I would like to recommend to anyone interested in theoretical aspects of gravitational lensing. In my opinion, the highlights are:

- A general method to exactly determine the propagation of scalar, electromagnetic and gravitational waves in space-times which are related to other "known" space-times via the transformation (14).
- An approximate version of it (end of section 3, and nicely illustrated in section 8), which shows in principle how to determine the propagation of waves in any space-time from their behavior in Minkowski.

- Page 3, last sentence of the paragraph after Eq. (7): The author argues that the source term on the right-hand side of (7) may be interpreted as being due to interference between neighboring rays. Could the author further explain that point? Same question for the remark after (108).
- Equation (14): This transformation is the core of the article. The author nicely explained its geometric meaning in appendix A. However, although I do trust the author on that point, the fact that such a metric transformation is the most general which preserves light rays does not seem to be explicitly proved in the article.
- End of section 3: Here the author somehow generalizes the previous results to any space-time, arguing that null waves in any space-time can be obtained from their counterpart in Minkowski space-time via diffeomorphisms. Is that equivalent to saying that, in a finite region of space-time, one can pick a coordinate system such that waves propagate in straight lines? If so, how does this method relate to Maartens’ observational coordinates, for instance, or the more recent geodesic light-cone method? In that context, the practical difficulty consists in finding the diffeomorphism leading to the desired metric. Does that also apply here?
- Section 8. This is really nice!

*[These comments were shared with us by a member of the cosmology community. They do not necessarily reflect the opinion of the Cosmo Comments team.]*