Black Hole Information Paradox without Hawking Radiation

Round 1

Reviewer 1 Report

please see attached file

Comments for author File: Comments.pdf

Author Response

I thank the reviewer for positive comments on my paper and for suggestions for further improvements.  My responses are the following.

In the revised version of the paper I better explain what do I mean by the statement that entropy is not necessarily thermal entropy.  In the first paragraph of Sec. 2 I add the sentence: "Namely, thermal entropy is entropy of systems in (or close to) thermal equilibrium, while many physical systems with entropy are far from thermal equilibrium." In addition, the first sentence of the next paragraph is extended to read: "The most interesting example is the entanglement entropy, which can characterize thermal and non-thermal systems."

In the revised version of the paper I also better explain why the energy can  be arbitrarily small, despite the quantization. After Eq. (2) I add the text: "(The energy of n photons of frequency ω is, in the physical units with \hbar not 1, equal to e = n\hbar ω. Even though n is integer, this energy can be arbitrarily small because ω can be arbitrarily small.)

In the Introduction of the revised version I also briefly explain what is meant by the information paradox.  In the first paragraph I add the following text: "Namely, the final state of Hawking radiation appears to be a mixed
thermal state, and purity of the full state cannot be encoded into entanglement between radiation and b.h. degrees of freedom, either because the b.h. evaporated completely, or the radiation contains more entropy than can be stored into the b.h. with a limited entropy capacity. Thus it looks as if the full state of the universe evolves from a pure initial state without Hawking radiation into a mixed state with radiation, which contradicts the general principle of unitarity, according to which pure states of closed quantum systems can evolve only into pure states." 

The reviewer also discussed in some detail a series of works, mostly by Parker and Jeynes. These papers are interesting on its own right. However, the reviewer didn't require that those papers should be cited in my paper and, in my opinion, those papers are not closely relevant to my paper. Hence I didn't cite them.

Reviewer 2 Report

It seems to be that this paper introduces a very novel approach on the information paradox based on the violations of the Bekenstein entropy bound. There are other instances where  violations of the Bekenstein entropy bound have been discussed, also involving very light modes, in this case because of very large extra dimensions in the interior of compact objects, see for example, 

DO EXTRA DIMENSIONS HAVE AN ENTROPY SIGNATURE? , E.I. Guendelman, David A. Owen, Published in: Phys.Lett.B 201 (1988) 297-300

the authors may consider comparing their arguments to those of that paper, otherwise the paper should be accepted

Author Response

I thank the reviewer for positive comments on my paper. The reviewer also mentioned another paper discussing one mechanism for violation of the Bekenstein bound (DO EXTRA DIMENSIONS HAVE AN ENTROPY SIGNATURE? , E.I. Guendelman, David A. Owen, Published in: Phys.Lett.B 201 (1988) 297-300) and suggested that "the authors may consider comparing their arguments to those of that paper". I think this paper is very interesting, but after a careful consideration I decided not to mention it in my paper. That's because in the paragraph after Eq. (6) I mention that there are other mechanisms for Bekenstein-bound violation and cite Ref. [19] where further references can be found. In my opinion, the mechanism by Guendelman and Owen is not more relevant to my paper than other mechanism in Ref. [19], so, since I didn't discuss explicitly those other mechanisms, it seemed consistent to me to not discuss the particular mechanism by Guendelman and Owen.

Reviewer 3 Report

Report on manuscript 2119168

“Black hole information paradox without Hawking radiation”

This manuscript studies the standard black hole information paradox without Hawking radiation. The manuscript has the potential to be published but after revision. I would like that the author addresses the following issues:

-       The author tried to keep the introduction short. It can be extended to add more information about Hawking radiation and discuss proposed solutions with Hawking radiation.

-       Line 80, 81: Please are a reference to support this statement (i.e. Bekenstein bound)

-       Author did not use proper citation style which made it difficult to check and follow with the references.

-       The author used “see ref.#, are studied in, ….”, which is ok but will be more readable to also summarize important information in the paper.

-       Line 160 – 162: please rephrase the sentence!

Author Response

Below I repeat the reviewer comments and give my responses.

Reviewer: The author tried to keep the introduction short. It can be extended to add more information about Hawking radiation and discuss proposed solutions with Hawking radiation.

Response: In the revised version of the paper I have significantly extended the first paragraph of Introduction.

Reviewer: Line 80, 81: Please are a reference to support this statement (i.e. Bekenstein bound)

Response: In the sentence before Eq. (4), I add reference [18].

Reviewer: Author did not use proper citation style which made it difficult to check and follow with the references.

Response: Different journals use different citation styles. The style I used is standard in at least some journals, e.g. in Physical Review D. I'm sure the stuff of the publisher associated with journal "Universe" will adjust the citation style to their own standards. 

Reviewer: The author used “see ref.#, are studied in, ….”, which is ok but will be more readable to also summarize important information in the paper.

Response: As far as I can see, I did not use this exact phrase anywhere in the paper. I would appreciate if the reviewer could specify more precisely the exact place where more details are needed.

Reviewer: Line 160 – 162: please rephrase the sentence!

Response: The first sentence in Sec. 4 now reads as follows: "The conclusion that any reasonable entropy bound can be violated by dropping sufficiently soft massless particles into the black hole is a paradox, so it needs to be
resolved."

Round 2

Reviewer 1 Report

This response of the Author looks very reasonable to me.

Reviewer 3 Report

The authors have addressed my comments from the previous review, and I recommend accepting it for publication