Black Holes Have More States than Those Defined by the Bekenstein–Hawking Entropy: A Simple Argument

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this short paper, the author concludes from a simple argument that the number of states of a black hole as evaluated by the Bekenstein-Hawking entropy is smaller than the actual number of states of the black hole as evaluated by an observer inside the black hole. This conclusion is not new, and it is not unacceptable to anyone, but there are points where the author's argument seems to be oversimplified, and a more precise discussion would be better. In the paragraph beginning on line 42, the author states that the area of the horizon is reduced by Hawking radiation, which is not necessarily compatible with the subsequent claim that the horizon is light-like. If the above issues were addressed with precision, the argument in this paragraph might not hold. Also, and this seems to be a simple mistake, N₂ in line 59 could be N₁.

Author Response

I thank the referee for emphasizing the subtleties due to the time-like nature of the horizon. I have rewritten the derivation taking these explicitly into account.  The derivation is cleaner now, in my opinion. 

Reviewer 2 Report

Comments and Suggestions for Authors

This article presents a very simple argument for a proposed discrepancy between the number of black hole states and the number of states counted by the Bekenstein--Hawking entropy. The entire elegant argument is contained between equations (1) and (3), while the rest of the article discusses physical implications of the result. The article is very well written, I would just recommend fixing the typo in the word  "convincing" in line 15. This paper will be interesting to a wide range of researchers working on black holes and quantum gravity, and I recommend this article for publication in Universe.

Author Response

Thanks for the correction.  Implemented. 

Reviewer 3 Report

Comments and Suggestions for Authors

The author presents a modification to the Bekenstein-Hawking entropy formula for black holes, showing that the number of states seen by observers inside the horizon exceeds the standard bound. I find the argument straight-forward and compelling. This will be of great interest to the quantum gravity community. I recommend publication of the manuscript in its present form.

Author Response

Thanks!

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

It seems that this manuscript is acceptable for publication in the journal without any major revisions.