Decoupled Embedding Class-One Strange Stars in Self-Interacting Brans–Dicke Gravity^†

Round 1

Reviewer 1 Report

In this manuscript the authors develop a study on Branes-Dicke gravity (BD), in the context of the so-called Gravitational Decoupling (GD), via minimal geometric deformation (MGD). The authors start from the equation of motions for BD in (7)-(9), supplemented by the wave equation for the scalar field in (10). Then, by using the GD approach, based on the metric decomposition (11), the authors manage to decouple the source specified in (16)-(18) from the original BD system (7)-(9). This introduces an immense simplification to study the BD system. Next, they apply what they obtained to solve a specific astrophysical problem: a quark star model. For this, the authors introduce a specific equation of state in (21). Subsequently, they introduce two additional restrictions: first a specific form for the scalar potential, and second, the so-called Karmakar condition. Finally, they produce two solutions by giving two specific form for the radial metric component, displayed in Eqs. (24) and (31), respectively. These solutions are analyzed in detail, finding that both are physically acceptable.

The manuscript presents an original work on BD gravity. They also use the gravitational decoupling approach, which is being widely used today. In particular, what surprises me is the level of simplification that GD introduces on a system as complicated as BD, where it is practically impossible to find analytical and physically acceptable solutions. In this sense, in my opinion, the work seems valuable and relevant, and in fact it can be extended in several ways (one would be considering the extended version of GD, for example).

My only criticism: the Gravitational decoupling approach was introduced in the seminal paper: Phys.Rev.D 95 (2017) 10, 104019, therefore the references [15] should be corrected.

With regard to references and minimal geometric deformation applied to complex forms of gravitational interaction, the authors should also cite two recently published articles, which are:

https://doi.org/10.1016/j.nuclphysb.2021.115420

https://doi.org/10.1103/PhysRevD.101.106002

I recommend the manuscript for publication after the above be corrected.

Author Response

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Reviewer 2 Report

I attached my report as a pdf file. 

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Round 2

Reviewer 2 Report

I have attached my second report as "universe-1221972-ugur-report_v2.pdf" file.

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Author Response

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