Capture of Massless and Massive Particles by Parameterized Black Holes
Round 1
Reviewer 1 Report
In this manuscript, the authors investigate the capture of massless and massive particles by the spherically symmetric black hole whose line element is described by the Rezzolla- Zhidenko parameterization by taking only the coefficient \varepsilon nonvanishing.
As far as I can see, the paper is reasonably clear, and some of the results are rather interesting. However, I find that some points are not clear. Therefore, before recommending this manuscript for publication, I would like the authors to consider the following points:
More explanation about the observational constraints associated with the values $a_0=b_0=0$.
Sylvester's matrix determinant is not shown correctly.
Author Response
We would like to thank the Referee for his/her comments that
surely improved the quality of the paper. In the revised version
of the manuscript we have edited the text of the paper based on
the points that were raised. We think that the revised version of
the manuscript addresses all the referee's comments and we hope
that the paper can now be considered suitable for publication in
Galaxies.
Detailed answers to the referee's comments/suggestions are
reported below.
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\textbf{\underline{Comment 1.:}} More explanation about the
observational constraints associated with the values $a_0=b_0=0$.
\textbf{\underline{Answer 1.:}} Indeed, throughout the paper we
adopted $a_0=b_0=0$. This choice of these parameters is motivated
from the Solar System tests of the general relativity at the first
post-Newtonian order. To obtain these constrains the followings
were done: (i) the first order asymptotic behaviours of metric
functions $g_{tt}$ and $g_{rr}$ were obtained in terms of the ADM
mass and the PPN parameters $\beta$, $\gamma$; (ii) by applying
well-known values of these PPN parameters (obtained by C. Will in
Ref. [1]) that constrained from the Solar System tests of general
relativity such as the perihelion precession of the orbit of the
planet Mercury (as $|1-\beta|\lesssim2.3\times10^{-4}$),
deflection of the light ray as it passes close to the sun (as
$|1-\gamma|\lesssim2.3\times10^{-5}$), one obtains that the values
of $a_0$ and $b_0$ are as small as $a_0\sim b_0\sim10^{-4}$. Since
these values are very small and in the strong field regime (when
$r$ is small), contributions of them to the spacetime metric is
negligible. Therefore, we adopted these constrains in the paper.
Since these all processes was explained with great details in Ref.
[10], we directed readers to that paper for details. Anyway, upon
a request of Referee, we included a few words on these constrains
to the paper.
\textbf{\underline{Comment 2.:}} Sylvester's matrix determinant is
not shown correctly.
\textbf{\underline{Answer 2.:}} We thank Referee for his this
comment. Indeed, in eq. (20) we wrote equation that comes from the
determinant of Sylvester's matrix (19) wrongly. In the revised
version we have corrected it.
We think that the revised version of the manuscript addresses the
point raised by Referee and we hope that the paper can now be
considered suitable for publication in Galaxies.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper deals with the interesting issue of the particle capture by spherical and static black holes. The comparisons are enlightening and the calculations are clear, whereby the results are interesting per se. The references are up-to-date. However, the conclusion section is too short and should be expanded, while there is need for a thorough and extensive editing of the English language (see also attached pdf-file).
Comments for author File: Comments.pdf
Author Response
We would like to thank the Referee for his/her comment and the
file in which our mistakes related to English grammar are shown.
We think that they surely improved the quality of the paper. In
the revised version of the manuscript we have extended conclusion
of the paper. Moreover, we have edited the text throughout the
paper under the instruction file sent by Referee. We think that
the revised version of the manuscript can now be considered
suitable for publication in Galaxies.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The authors have complied with my earlier suggestions and the manuscript is largely improved.
After (a) fitting eq.(19) on the page so that it can be seen better, (b) adding a comma right after orbits in line 202, and (c) correcting terms to term in line 208.
Author Response
We thank Referee one more time for his efforts that have increased the quality of our paper. In the revised version we addressed all the comments raised by Referee.
