Review Reports

Round 1

Reviewer 1 Report

I congrutulate the AUTHORS they presentes a beautiful Pierce of interconnection between their and exp in Gás nesses this is ah interesting tópico which há a been recently been used by testing modified gravity by comparou their projection to GWs

Author Response

We are grateful to the referee for the time devoted to read and review our paper. As we understand the report, the conslusion is positive, hence we thank the referee very much.

Reviewer 2 Report

The review paper raises the interesting and actual questions of the possibilities to detect "black hole" by their strong gravitational lensing appearances, it is good structured and written in a clearly understandable way. I think it can be published in its present form.

Author Response

We are grateful to the referee for the positive assessment of our paper.

Reviewer 3 Report

The paper gave a good review on the subject of gravitational lensing of gravitational waves, the paper is well organized and well written, I recommend it to be accepted at the present form.

Author Response

We are grateful to the referee for the positive assessment of our paper.

Reviewer 4 Report

In this paper, the authors studied the cosmological and astrophysical traces in the gravitational lensing of gravitational waves.  Each section is well-argued and the observational values are detailed through calculations and plots. I recommend publishing in the present form.

Author Response

We are grateful to the referee for the positive assessment of our paper.

Reviewer 5 Report

The paper is a review of gravitational lensing applied to gravitational waves. Gravitational lensing is reviewed from the point of view of wave optics as well as gravitational optics. The lens model considered are the point mass lens and the singular isothermal sphere model. Possible predictions of GW lensing are then reviewed and compared with the present and future GW experiments. The final part of the review is devoted to the possible applications of these results to the present main hot cosmological and astrophysical problems: tests concerning cosmological models and dark matter.

My opinion is that this review is excellent and I recommend its publication on Universe. I would only like to signal a few (possible) typos:

- second line after eq.(12): the symbols $n_j, n_k$ are not explained

- first paragraph of (2.2): frequency is denoted both by w and by $\omega$

- third line after eq.(35): should not "approaches infinity" be replaced by "approaches 0" ?

Author Response

We are grateful to the referee for the positive assessment of our paper. In particular, we appreciate good and constructive comments.
Comment 1 - we thank the referee for careful reading and noticing this typo. The symbols n_i n_j were remainders of the preliminary draft, which we overlooked. We apologize for that and thank the referee again. In the final version we deleted this redundant unnecessary phrase.
Comment 2 - we thank the referee for very careful reading. Indeed similar appearance of "w" and "omega" might raise the confusion. However, what has been writtten is right: "w" is a dimensionless frequency (defined in Eq.10) and is here a proper criterion of validity of wave and geometric optics regimes. The difference with just "omega" is subtle as involves the properties of the lensing system as well (in particular the mass of the lens - see e.g. Eq.23). On the other hand for comparison between light and GWs - second bracket - the relation of frequencies are relevant (tacitly assuming the same lensing configuration). We have added a few words elucidating this.
Comment 3 - the essence of this comment is that the total mass of the lens obtained by integration over radial coordinate to infinity diverges. We tried to reformulate this sentence in order to make it more understandable.