Gauge-Invariant Perturbation Theory on the Schwarzschild Background Spacetime Part I: Formulation and Odd-Mode Perturbations

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript has issues:

[1] The statement “there is no preferred coordinate system in nature” is a false statement. Black Holes are spacelike matter and acausal, which means spacelike matter has no covariant equations describing it.

[2] Gauge invariant perturbation theory in this manuscript is very confusing:  Perturbation theory involves small changes in observables, not coordinate transformations. For example, one measures the radar cross section of a metal plate. Then putting a hole in that plate is a perturbation on the original radar cross section; it has nothing to do with coordinate transformations.

[3] The Universe Journal is not the appropriate journal for this 61 page manuscript that has no physics content. It should be sent to a pure mathematics journal.

Author Response

The response to comments from the Reviewer 1 is described in the attached pdf file.

See the attached pdf file.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

See attached PDF.

Comments for author File: Comments.pdf

Author Response

The responses to comments from Reviewer 2 are summarized in the attached pdf file.

See the attached pdf file.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

As part  of our series of papers on a gauge-invariant “linear” perturbation theory on the Schwarzschild background spacetime, authors review the general framework of the gauge-invariant perturbation theory. Paper is well written and provides sufficient scientific knowledge. Authors should check some correction may be required:

1. After Eq.7, while citing the equation authors, some times use equation (7) and some time EQ. (7). It should be the same. Its an example; that authors should check the whole paper.

2. In some places at the end of sentences ending before equations, authors end with ":" like at the end of a sentence before eq. 38, while in other places they do not. It should be the same everywhere.

Otherwise, the paper is well written with interesting knowledge.

 

 

Author Response

Dear Reviewer 3 of universe-3305559,

 

I appreciate your review report.

I am sending my response to your report.

My response is written in the attached pdf file.

 

Sincerely Yours,

Kouji Nakamura

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Please see the attached report

Comments for author File: Comments.pdf

Author Response

Dear Reviewer 4 of universe-3305559,

 

I appreciate your review report.

I am sending my response to your report.

My report is written in the attached pdf file.

 

Sincerely Yours,

Kouji Nakamura

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript has no useful physics: An accretion disk in elliptical orbit about a Black Hole creates a complicated self-energy gravitational potential, but there is nothing in the manuscript that would allow me to compute this self-energy. Furthermore the static Schwarzchild solution has scalar curvature R = 0, but the presence of gravitational waves mean there is now time dependence and a non-zero R. How do I renormalize R?

I challenge any physicist who reads this manuscript to gleam any useful technique that solves a real astrophysical problem.

Author Response

The response to the 2nd Round Comments from Reviewer 1 is written in the attached pdf file.

Author Response File: Author Response.pdf