Study of a Minimally Deformed Anisotropic Solution for Compact Objects with Massive Scalar Field in Brans–Dicke Gravity Admitting the Karmarkar Condition

Round 1

Reviewer 1 Report

Dear authors

i have read your work and obtained it suitable but before to publish it in the  journal it is appropriate  that you check some minor revisions as pointed at below.

What is ? in page 13 , line 371....[88?-90]

In the reference [29] : Author`s name should be corrected as S. K. Maurya

sincerely

 

Author Response

Reviewer 1:
I have read your work and obtained it suitable but before publishing it in the journal it is appropriate that you check some minor revisions as pointed out below.
Ans: We would like to express our sincere gratitude to the anonymous referee for his/her positive report.
Q1. What is ? in page 13 , line 371....[88?-90].
Ans: We have corrected it .
Q2. In the reference [29] : Author‘s name should be corrected as S. K. Maurya:
Ans: We have corrected the typo.

Reviewer 2 Report

In the present manuscript, authors have investigated anisotropic exact solutions in the context of massive Brans-Dicke theory of gravity. Paper is interesting and calculations seem accurate, but I have few concerns about their work:

1. In action, what is L(\phi)? Is it an alternate notation for scalar field potential? Since they considered framework as massive so the scalar field must have non-zero potential. Authors should explain this notation.

2. In literature, I have seen two prominent techniques to find exact stellar solutions: one is the use of well-known Karmarkar condition which provides a relationship between the two metric potentials and then by assuming some well-known form of one of the metric coefficients (like they assumed Finch-Skea model), second one can be easily computed. In this case, the only unknowns left will be matter density and anisotropic pressures (as they assumed a power law type of scalar field potential as well) which can be computed through field equations and then different features of the model can be easily investigated.

Second technique is MGD (minimal gravitational decoupling) where a new sector is introduced and some transformation for metric potential is introduced. In my opinion, only one of these techniques have been used in all past papers, not both techniques at the same time. What is the need and motivation to use both strategies together for finding the solution?

3. Authors have computed scalar field wave equation (7). I believe that in this equation, one needs to use the trace of Eq. (6) so there must appear a term due to additional introduced new sector  ᶿ.

Authors should re-check this equation and explain its derivation.  

4. Authors should put some light on the impact of BD parameter and the inclusion of scalar field potential (massive) in their study. There are many discussions available on the BD parameter values, i.e., what is the most accurate value for this parameter. Authors must explain the importance of the value they assigned to BD parameter (ꙍBD=5) in their graphing analysis (what will happen if they change its value to a very small or a large number)?  

5. I believe that there are many past related works available on the same topic so authors should add some comparison with these works and highlights novelty and significance of their work.

 Authors should answer these questions in detail and modify their paper accordingly. After these amendments, this paper can be considered for publication in this  scientific journal.

 

 

  

 

Author Response

In the present manuscript, authors have investigated anisotropic exact solutions in the context of massive Brans-Dicke theory of gravity. The paper is interesting and calculations seem accurate, but I have few concerns about their work:
Ans: We would like to express our sincere gratitude to the anonymous referee for his/her positive report.

Q1. In action, what is L(ϕ)? Is it an alternate notation for scalar field potential? Since they considered framework as massive so the scalar field must have non-zero potential.
Authors should explain this notation.
Ans: Yes, L(φ) is an alternate notation of L(ϕ) used in the present article which is a non-zero scalar field. We have defined it after Eq.(42).
Q2. In literature, I have seen two prominent techniques to find exact stellar solutions: one is the use of well-known Karmarkar condition which provides a relationship between
the two metric potentials, and then by assuming some well-known form of one of the metric coefficients (like they assumed Finch-Skea model), the second one can be easily
computed. In this case, the only unknowns left will be matter density and anisotropic pressures (as they assumed a power law type of scalar field potential as well) which can
be computed through field equations and then different features of the model can be easily investigated.
The second technique is MGD (minimal gravitational decoupling) where a new sector is introduced and some transformation for metric potential is introduced. In my opinion, only one of these techniques has been used in all past papers, not both techniques at the same time. What is the need and motivation to use both strategies together for finding the solution?
Ans: We appreciate the anonymous reviewer for raising this important point. In the present article, our objective is to find the solution using gravitational decoupling. As
we know that the MGD technique allows obtaining the solution beyond the chosen gravity. Furthermore, the MGD approach divides the original system into two parts,
the first system corresponds to pure Brans-Dicke gravity while the second system is due to gravitational decoupling. We have assumed the internal structure of the first
system is made of anisotropic fluid matter distribution rather than isotropic matter distribution. Therefore we need two extra conditions to solve the first system. Due to this reason, we have used the embedding class one condition (Karmarkar condition) along with the radial metric function corresponding to the Finch-Skea model to solve the first system while the second system is solved by using the mimic constraints approach. Finally,
we get the solution of the original system after combining the solutions of both systems which is the generalization of embedding class I solution beyond the Brans-Dicke gravity.
Q3. Authors have computed the scalar field wave equation (7). I believe that in this equation, one needs to use the trace of Eq. (6) so there must appear a term due to the additional introduced new sector θ. The authors should re-check this equation and explain its derivation.
Ans: We are sorry for this mistake. We have corrected it.
Q4. Authors should put some light on the impact of BD parameters and the inclusion of scalar field potential (massive) in their study. There are many discussions available on the BD parameter values, i.e., what is the most accurate value for this parameter? Authors must explain the importance of the value they assigned to BD parameter (ωBD = 5) in their graphing analysis (what will happen if they change its value to a very small or a large number)?
Ans: We have mentioned the impact of BD parameter on thermodynamical properties (see highlighted blue color portion from section VII).
Q5. I believe that there are many past related works available on the same topic so authors should add some comparison with these works and highlights novelty and significance of their work.
Ans: We have added some works on the Brans-Dicke gravity.

Reviewer 3 Report

Dear Authors,

I reviewed the article titled Minimally deformed anisotropic solution study for compact objects with massive scalar field in Brans-Dicke gravity accepting Karmarkar condition.

 

In this paper, the Authors focused on exploring the possibility of providing a new class of exact solutions for living anisotropic star systems through the Brans-Dicke (BD) theory of gravity. In this context, they used decomposition of gravity sources with minimal geometric deformation (MGD) ($e^{-\eta}=\Psi+\beta\,h$) for compact star objects in the class embedding area.

Some inaccuracies and printing errors in the article should be corrected,

eg.

Like 45 equations.

I think that the manuscript can be accepted for publication at Univers with minor corrections.

Author Response

In this paper, the Authors focused on exploring the possibility of providing a new class of exact solutions for living anisotropic star systems through the Brans-Dicke (BD) theory of gravity. In this context, they used decomposition of gravity sources with minimal
geometric deformation (MGD) (e^−η = Ψ + β h) for compact star objects in the class embedding area. Some inaccuracies and printing errors in the article should be corrected, e.g. Like 45 equations.
Ans: We have corrected the typos.

Reviewer 4 Report

The authors have obtained the anisotropic solution for compact objects using gravitational decoupling in the context of Brans-Dicke gravity satisfying the Karmarkar condition. The paper is well-written and deserves for publication after addressing the following points:

1. The authors need to review the literature and include some more recent works on modified gravity theory in the context of gravitational decoupling.

2. The author has used the two constraints (i) mimic to pressure constraint (ii) mimic to density constraint. It is better to author explains the importance of these approaches.

3. The authors have plotted the M-R curve to predict the radii for several different stellar objects. However, it is not mentioned in the text rather than the maximum mass. Therefore, I encourage the authors to include the table for the M-R curves.

4. I encourage the author to enhance the conclusion by including a section for predicted radii with observational findings.

After addressing the following points, the paper can be accepted for publication. 

 

Author Response

The authors have obtained the anisotropic solution for compact objects using gravitational decoupling in the context of Brans-Dicke gravity satisfying the Karmarkar condition. The paper is well-written and deserves publication after addressing the following points:
Ans: We would like to express our sincere gratitude to the anonymous referee for his/her positive report.
Q1. The authors need to review the literature and include some more recent works on modified gravity theory in the context of gravitational decoupling.
Ans: we have included some works in modified gravity theory in the context of gravitational decoupling.
Q2. The author has used two constraints (i) mimic to pressure constraint (ii) mimic to density constraint. It is better to author explains the importance of these approaches.
Ans: We have mentioned the importance of both approaches in section VI.
Q3. The authors have plotted the M-R curve to predict the radii for several different stellar objects. However, it is not mentioned in the text rather than the maximum mass.
Therefore, I encourage the authors to include the table for the M-R curves.
Ans: We have included a table related for Figs. 15 and 16 to predict the radii for different values fo few parameters.
Q4. I encourage the author to enhance the conclusion by including a section for predicted radii with observational findings.
Ans: We have included some discussion regarding the predicted radii with observational findings.

Round 2

Reviewer 2 Report

Following my comments in 1st report, authors have substantially improved the overall presentation of this manuscript. In its present form, article can be accepted for publication in this scientific journal.