Can Effects of a Generalized Uncertainty Principle Appear in Compact Stars?

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The work is very interesting and highlights the connection between quantum gravity, nuclear physics, and astrophysics. Although the Walecka model is quite simple and without isospin dependence not appropriate to describe neutron stars, its use is understandable as a first approach to the problem. 

I recommend the paper for publication after some minor issues are addressed:

- some variables such as the nucleon mass and degeneracy factor are not defined

- there is no explanation about how the beta correction for dx^N dp^N remains the same correction for dk^3

- the pressure and energy density in Eq (34) are presented in different stages of integration (one still has dk^3, while the other already has dk). They should be presented at the same stage

- it is never said if beta*p^2<<1 is a reasonable approximation for the beta values used in this paper

- not all lines are visible in Fig 2

- why do the different figures present different values of beta?

Author Response

"Please see the attachment."

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors In the present work, the authors provide a preliminary analysis of the
effects of the Generalized Uncertainty Principle (GUP) with a minimum length, in the context of compact stars. In particular, they introduce the non-commutative effects on the neutron star equation of state and systematically study these effect on the bulk neutron stars properties. The presentation is well written concerning both the quantum mechanical, statistical mechanics and the nuclear physics part. Moreover, some interesting new results are provided while the bibliography is adequate and complete. This is a novel application of the GUP in compact objects and I would like to recommend the publication of this paper but not in its present form. I suggest the authors to consider, in the revised version, the following points:     1) The results in figure 6 correspond to the case of neutron stars without crust. Although the main conclusions may not change, the author must to comment about it. In the same figure the case $\beta=3 \times 10^{-2}$ fm$^2$ the corresponding curve does not reach the maximum mass. Is there any explanation ?   2) The discussion of the results (mainly those presented in figures 1-6) are very limited. I would like to recommend the authors to make a more extensive presentation of the results, giving more weight to the physics that one can derive from the relative diagrams, since this is the main aim of the paper. In the same direction is my comment about the captions on the figures. They are very poor and do not fully describe the figures.   3) In general the quality of the figures in not appropriate (for example see figure 3, the vertical axis). Moreover in each figure they use the notation $\gamma= 4$ (Nuclear Matter) (please clarify the meaning). It is not necessary to use it in each figure. It is sufficient you mention it once.   4) In some cases, from the figures it follows that holds the inequality $dP/d\epsilon<0$. This condition introduce problems of thermodynamic stability in the equation of state and consequently on the structure of neutron stars. Please, clarify and comment about this crucial point.      

 

 

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors responded comprehensively to the points I raised and provided clarifications where necessary. Additionally, they implemented further improvements to the work. Based on these efforts, I recommend the publication of the work in its current form.