Noncommutative Reissner–Nordström Black Hole from Noncommutative Charged Scalar Field
, Andjelo Samsarov 2 and Ivica Smolić 3
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsPlease see the attached PDF file.
Comments for author File: 
Comments.pdf
Author Response
We thank the reviewer for all the comments and suggestions.
Regarding the first comment: the SW map in our particular model (so NC defined by angular twist, RN background and charged scalar field) stops at the second order. The third, fourth, etc. order corrections to the equation of motion for the scalar field are 0. This is due to the simplicity of the \Theta tensor, the fact that EM field has only one component (see 11) and fixed RN background.
Also, the dispersion relation for scalar field in our model is undeformed, the NC correction appears in the interaction term between the scalar and EM field.
We added more details on the derivation on page 3, eq.(7), and a paragraph on page 5 after (18).
Regarding the second comment:
we thank the reviewer for this comment, we added these references.
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper reviews an interesting proposal to investigate the effects
on the physics of black holes of a specific model of noncommutative
geometry through the deformation of the Klein-Gordon equation and the
ensuing definition of an effective metric.
The results and the discussion are relevant for the understanding of
the possible outcomes of noncommutative geometry on black-hole physics.
The exposition is good, except for several typos.
However, a couple of questions are not clear and should be explained
in more detail:
- In various points it is claimed that the second-order expansion is
exact, but no justification is given of this claim. Is this a result
of the computations or a property of the Seiberg-Witten expansion?
- Moreover, is the effective metric deduced in the paper specific of
scalar fields or it holds also for higher-spin fields?
If the authors add some comments on these points, the paper certainly
deserves publication on Symmetry.
Author Response
We thank the reviewer for all the comments.
Regarding SW: due to the simplicity of our model (special NC defined by the simple Theta tensor, fixed RN background and equation of motion for the charged scalar field ) the third and higher orders are 0.
We added more details and comments on page 3 and page 5.
Regarding the construction of effective metric for other fields: we added a comment on this on page 6. Namely, for the spin 1/2 things function in the analogous way as in the scalar field, ultimately leading to the same effective metric. For the spin 1 field one is unable to do the same because the NC correction to the equation of motion for vector field are of "Yang-Mills type", i.e. nonlinear in the field.
Reviewer 3 Report
Comments and Suggestions for AuthorsSee attached file
Comments for author File: Comments.pdf
Author Response
We thank the reviewer for the comments and we implement the minor comment in the Introduction.
Reviewer 4 Report
Comments and Suggestions for AuthorsThe paper presents a detailed study of the noncommutative (NC) deformation of the Reissner–Nordström (RN) metric by utilizing the Seiberg-Witten (SW) map. It constructs a noncommutative scalar and gauge field model up to the second order in the deformation parameter and demonstrates that the second-order expansion is exact and nonperturbative. The paper addresses a highly relevant topic in the intersection of black hole physics, quantum gravity, and noncommutative geometry. Its methods and results are technically sound.
Minor Comments:
1. Clarity in Derivations:
Some derivations, particularly those leading to Equation (14), are dense and could be expanded for clarity.
Suggestion: Include intermediate steps and explicitly connect the SW map to the deformation of the RN metric to help readers follow the logical progression.
2. Check for Typographical Errors:
Ensure all symbols and parameters (e.g., deformation parameter 𝜃 or 𝑎) are consistently defined and used throughout the paper.
Author Response
We thank the reviewer for the comments.
Regarding 1: we added more details and comments on page 3, 4 and 5
Regarding 2: the relation between Theta and a is given in the text after eq.(5)
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe respectful authors have addressed my comments. I recommend publication of this manuscript in its present revised form.
