Probing the Lorentz Invariance Violation via Gravitational Lensing and Analytical Eigenmodes of Perturbed Slowly Rotating Bumblebee Black Holes
Round 1
Reviewer 1 Report
Comments for author File: 
Comments.pdf
Author Response
Dear Reviewer, thank you for your comments. Please see the attached pdf file, which include our responses. Best Regards.
Author Response File: Author Response.pdf
Reviewer 2 Report
This paper Is written on a subject that might be interesting in the face of of present black hole observations. It is on consequences of approximate black hole solutions of the "bumblebee model", introduced as a toy model by Kostelecky, who should be cited. Scattered along the paper there are strange statements, for example that the bumblebee field is scalar, just at the beginning of the second paragraph of the introduction. However, the first part of second section "RBBH spacetime", is completely nonsense, as if the authors would try to mislead wholly unaware readers. In any case, this part is a copy that badly worsens errors and wrong formulations of the provided reference [45], all that along almost two pages. In fact, in reference [19] these developments are correctly done. I am not going to enter farther into the details of this piece. After that, the authors present the black hole solution (11) of reference [19], as if it would be a wright solution, to state then that this is not a solution, without citing the original comment of Maluf and Muniz, who proved it. Regarding that, equation (11) is again a bad copy of the one of reference [19].
It is possible that the further developments of this paper, on properties of the approximate solution (16), regarding thermodynamics and effects of Lorentz symmetry breaking on gravitational lensing, and emission of radiation. However, due to the previously mentioned shortcomings, we cannot rely on these results, without verification of lengthy details of the computations, that are not purpose of a revision of the paper.
Therefore, I do not recommend to publish this paper in Universe.
Author Response
Dear Reviewer, thank you for your comments. Please see the attached pdf file, which include our responses. Best Regards.
Author Response File: Author Response.pdf
Reviewer 3 Report
In this paper, the authors studied the potential of probing Lorentz Invariance Violationthrough the gravitational lensing, GFs, and QNMs of slow-spinning Bumblebee Black Holes. In these four dimensions, the authors give the corresponding results. Before however deciding about the publication of this manuscript, I would like the authors to address the following points:
1. The author discusses 4 aspects, but it seems that each aspect of the research is independent, so the author should discuss the links between them in depth, otherwise the whole article appears to be a simple patchwork of multiple research efforts.
2. This paper discusses the effect of LIV on the properties of black holes. In fact, there are many works discussing the effect of quantum gravity effect on black holes, such as arxiv:1810.05645, arXiv:1604.04702, arXiv:hep-ph/0701043 , arXiv:2206.08601, etc. I suggest the authors to compare their work with these works and discuss the innovativeness of this paper.
3. The third item on the right hand side of Eq. (11) looks incorrect, please confirm.
4. There are also some typos in the paper.
Author Response
Dear Reviewer, thank you for your comments. Please see the attached pdf file, which include our responses. Best Regards.
Author Response File: Author Response.pdf
Reviewer 4 Report
The paper is devoted to study of a number of properties of a slowly rotating black hole within the scope of the so-called Bumblebee gravity, which involves the Lorentz invariance violation. The paper is clearly written, it seems to be mathematically correct, and can be of interest for scientific community working in this research field.
There are some minor remarks concerning the presentation of the results.
1. What is the difference between quantities $R_{ab} and ${\cal R}_{ab}$ in Eqs. (4)-(9)?
2. There are some undefined labels marked by "??": in the caption under Fig. 1, and in the line after Eq. (49); and also "[xx]" before Eq.(30).
3. In some places, there is "ell" instead of "$\ell$", namely, in lines 170, 198, 200, 203, 216.
4. What system of units is used in the text? In particular, which unit is used for $\omega$ in the plots?
5. There is a typo "M=m1" in the caption of Fig. 4.
6. What is "L" in Eq. (77)?
The points above are just about the style of presentation, and do not concern the overall quality / significance of the research, which is definitely deserves publication in my view. I believe that after addressing these minor remarks the paper can be published.
Author Response
Dear Reviewer, thank you for your comments. Please see the attached pdf file, which include our responses. Best Regards.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
In their response the authors mention their experience in the considered model, undoubtedly it is so, but I still have several, not exhaustive, observations that show at least neglect from the authors in the redaction and citing:
Line 25: it is stated that the bumblebee field is scalar.
The notation of the potential is sometimes V and sometimes \cal V.
In eq. (12) there is a factor 1+ℓ that should not be there.
In the line 165 there is a misplaced θ=π/2
Before eq. (55) there is a misplaced sentence "and applying the following ansatz".
Since the previous version, eq. (7) has an error due to a copy-paste from eq. (6) of ref. [45], without verifying the equation. In fact, the correct equation is as in eq. (2.5) of ref. [19].
Similarly, in the previous version of the paper, eq. (9) has been copied exactly from eq. (9) of ref. [45]. However, in the paper under revision it is stated wrongly that (9) follows from (8), instead of that this equation defines \bar{R}, as given in [45]. In the new version a slight change has been made in (9): \bar{R} → R, but the equation is still given as following from (8).
I recommend that the authors revise careful and responsibly the paper before publication.
Author Response
Dear Referee,
Thank you for your comments and positive criticisms. Our responses are in the attached file. Best Regards, Authors
Author Response File: Author Response.pdf
Reviewer 3 Report
In the revised version the authors have fulfilled all my raised points, and thus I recommend the paper for publication.
Author Response
Dear Referee,
Thank you for your comments and positive criticisms. Our responses are in the attached file. Best Regards, Authors
Author Response File: Author Response.pdf
