The Negative Energy in Generalized Vaidya Spacetime
Round 1
Reviewer 1 Report
The author considers the existence of negative energy in the the generalized Vaidya spacetime in the context of gravitational collapse. It is shown that negative energy is possible in a particular range, and this is forbidden in the case of naked singularity formation. The results are interesting and will be of interest to researchers involved in this area of research. A revised version may be considered for publication once the following points are addressed:
- There are numerous typographical and grammatical mistakes (too many to list). The paper needs to be carefully checked and corrected.
- The material presented in sections 2 and 3 of the paper is mainly background. This is too long and should be summarized; only the main results are necessary. For example it is not necessary to give the various components in (22)-(27) as they are standard.
- Some more discussion should be provided on the physical consequences of the results obtained. How do the results differ from other investigations, and the normal Vaidya spacetime in particular?
A revised manuscript addressing these points may be reconsidered for publication.
Author Response
First of all I would like to thank the reviewer for reading this paper and helpful comments. Unfortunately I can't point out the correction what I have done in pdf because I am blind and it is impossible for me to work with pdf file. So I will write all correction which have been done.
1. I carefully read the text and corrected numerous mistakes in text and formulas. The mistakes in formulas are just missprints and they don't have impact on the results obtained in this article. Also doubled spaces have been removed.
2. I have also corrected indices in formulas.
3. Formulas devoted to the naked singularity formation have been removed because in this paper only the negative energy problem is considered. Also the metric components and connected tensors components in generalized Vaidya spacetime have been removed because they are too obvious.
4. The section'Discussion' have been totally rewritten.
Now I would like to answer the comments:
1. There are numerous typographical and grammatical mistakes (too many to list). The paper needs to be carefully checked and corrected.
'I have read the article and corrected mistakes in the text. Also I found out missprints in formulas and corrected them.'
2. The material presented in sections 2 and 3 of the paper is mainly background. This is too long and should be summarized; only the main results are
necessary. For example it is not necessary to give the various components in (22)-(27) as they are standard.
'Various components have been removed. Also the methods devoted to naked singularity formation have been removed because in this paper only the negative energy problem is considered.'
3. Some more discussion should be provided on the physical consequences of the results obtained. How do the results differ from other investigations, and
the normal Vaidya spacetime in particular?
'The section Discussion has been totally rewritten. Vaidya spacetime is a particular case of the generalized Vaidya spacetime and the results obtained in this paper are also valid in the case of normal Vaidya spacetime. I have pointed out it in new discussion section.'
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The article is not a completed work. Rather, it is a rough sketch. The text is not proofread; ill-conceived phrases are added to the typos that contradict scientific research. There is no sufficient justification for the results obtained. Some formulas are written out with errors. There is a repeated, unreasonable repetition of formulas, there is no clear system of indices, data are given that are not necessary. The result of the research done is vaguely spelled out.
Author Response
First of all I would like to thank the reviewer for careful reading and very important comments. I am really sorry for this poor english text. I am blind and my special program didn't tell me that there were numerous mistakes. I have corrected the paper but I can't read pdf file and i am not able to point out in pdf what I have corrected. So I will write below what corrections i have done.
1. I carefully read with the help of sighted people the text and corrected numerous mistakes in text and formulas. The mistakes in formulas are just missprints and they don't have impact on the results obtained in this article. Also doubled spaces have been removed.
2. I have also corrected indices in formulas.
3. Formulas devoted to the naked singularity formation have been removed because in this paper only the negative energy problem is considered. Also the metric components and connected tensors components in generalized Vaidya spacetime have been removed because they are too obvious.
4. The section'Discussion' have been totally rewritten.
Unfortunately to prove the absence of the particles with negative energy in the case of the naked singularity formation we have to use similar formulas which differ from each other only by sign.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The author has a made a good attempt at addressing the corrections and other issues highlighted in the first review. The paper may be accepted for publication.
Author Response
I would like to thank the reviewer for very helpful comments and suggestions.
Reviewer 2 Report
The article became more clear and readable. Neverthelaess, there are still many misprints and confusion in text. I will list my suggestions.
Introduction. Page 1, line 23. S. Maharaj is not the first author. Better to write: M. Mkenyley et al.// Page 2, line 34. I recommend to use the term "Type-I", etc./ Lines 44-47. It should be Arabic numbers for sections./ Line 48: ...units g change for G - Newton gravitational constant.
Section 2. Page 2, line 50. I suggest to change the title of the section. As version "Geodesic equation, energy and angular momentum"./ Line 51-52. I do not agree that this is purely mathematical work. The work is based on differntial geometry apparatus but contain physics approach: motion (geodesics), energy, momentum./ Line 55-56, formula (4), first term is the second derivation./ Line 59. $g_{ig}$ change for $g_{ik}$./ Line 61-62, formula (8). 1/2 should be power of r.h.s., not multiplier./Line 86. Morover there (not the) must .../
Section 3. Page 7, formula (14) - check k-index (in first two lines) and i-index in 8 line in the formula. / Line 150. ...this case in this paper - improve. Page 8, lines 163-166. To calculate the expantion $\Theta$ wich is (25) Now using (23)... - improve./
Section 4. Page 9, lines 176-179. Uppercase or lowercase letters?/ line 199, formula (34) 1-st line in , R or r?/ Line 202-203 Incompressible sentence. You can prove it in another article?/ Line 204-205, formula (36). Once again 1/2 should be power./formula (37) check $(\dot\varphi)^2$ in rhs. / Line 208-209. Partial ? derivative./ Line 221. "it means" change to "It means".
Section 5. Lines 276, 277. In this case... In this case...
Author Response
I would like to thank the reviewer for very helpful comments and suggestions. I have corrected all missprints which the reviewer pointed out.
I haven't changed only formula (8). There are 2 ways to write this formula. I use Chandrasekhar way to obtain the energy and the angular momentum. In Chandrasekhar's book it was shown that we can use this formula (See, for example chapter I,III and VII S. Chandrasekhar, The Mathematical Theory of Black Holes (Clarendon Press, Oxford University Press, New York, Oxford, 1983). ). In the text below this formula I also give a link for a textbook where there is the proof of the equivalence of these two formulas.
