Null and Timelike Geodesics near the Throats of Phantom Scalar Field Wormholesâ€
Round 1
Reviewer 1 Report
The paper under refereeing is devoted to a very interesting subject directly related to observational properties of wormholes which may help to distinguish them from black holes or other compact objects. In my opinion, the results are convincing and useful, the paper is well and clearly written, thus I have no doubt that it deserves being published. There are only a few small remarks to be addressed before that.
1. In Eq. (13), in the Taylor expansions near $r=0$, two coefficients should be
1/4! = 1/24 instead of 1/6.
2. In captions to Figs. 4 and 5 there is a strange phrase "Photon trajectories
$C(\varphi)$ of massive test particles....". I suppose that these are simply photon trajectories.
3. At the very end of Sec. 4, discussing what a distant observer can see, I think, one could mention possible photons coming from "the other universe" through the wormhole (even though an accretion disk should look much brighter).
4. The authors discuss the properties of wormholes symmetric with respect to the throat. Still it seems reasonable to mention a study comparing lensing by symmetric and asymmetric wormholes [arXiv: 1812.05704; Grav. Cosmol. 25, 44 (2019)]. Also, to a discussion of the inverse problem method used by the authors: it was probably used for the first time to find solutions for the system (1) in Ref. [31] but only for a canonical scalar field, while for the phantom case it was first used in [gr-qc/0511109, PRL 96, 251101 (2006)]
and in many later papers; all that probably deserves some mentioning.
5. The notations are certainly a matter of taste; still, to be frank, while reading, I feel discomfort with the spherical radius denoted by $C$ (usually percieved as a notation for constants). In my work I prefer the natural notation $r$ for the radius ($r^2=|g_{22}|$) and another letter, say,
$x$ or $u$, for a radial coordinate which can be arbitrary. This remark can of course be ignored.
Conclusion: in my opinion, the paper can be published after minor amendment subject to the above remarks.
Author Response
Please, find our reply in the file Corrections.pdf,
and find the corrected version of the manuscript in the file TsirulevAN_Corrections.pdf
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Please, for the report review for the authors see the attached PDF file.
Comments for author File: Comments.pdf
Author Response
Please, find our reply in the file Corrections.pdf,
and find the corrected version of the manuscript in the file TsirulevAN_Corrections.pdf.
All corrections are highlighted by blue clour.
Author Response File: Author Response.pdf
Reviewer 3 Report
There is no special comments or suggestions. Perhaps, the only thing, is that not to use the notation "radial" for the coordinate which can be negative. But this decision, of course, is up to the authors.
Author Response
Please, find our reply in the file Corrections.pdf,
and find the corrected version of the manuscript in the file TsirulevAN_Corrections.pdf.
All corrections are highlighted by blue clour.
Author Response File: Author Response.pdf
Reviewer 4 Report
The authors of the paper study the geodesic motion of photons and particles near the throat of asymptotically flat, static, spherically symmetric traversable wormhole supported by a self-gravitating minimally coupled phantom scalar field with an arbitrary self-interaction potential. The main results obtained by the authors are fundamental for understanding the phenomena related to the distribution and interaction of the substances in the vicinity of exotic compact objects and therefore deserves to be published in the journal. The authors also consider what could be the observational consequences of the considered model.
Author Response
Please, find our reply in the file Corrections.pdf,
and find the corrected version of the manuscript in the file TsirulevAN_Corrections.pdf.
All corrections are highlighted by blue clour.
Author Response File: Author Response.pdf
