A line in the article states that "the event horizon area of a black hole cannot decrease". However due to Hawking Radiation, microscopic black holes should theoretically grow smaller and vanish. While its a small point; shouldn't the article differentiate between macroscopic and microscopic behavior?
Only two minor suggestions:
1- After equation (12) I would rather say that the content of the GSL is the area theorem in the classical limit. This is because it is not possible to avoid ordinary entropy in the quantum case due to Hawking radiation, and on the other hand the area theorem works also when there is external matter entropy if it satisfies the appropriate energy condition.
2- I would repeat the citation to Bombelli et al in the section dedicated to entanglement entropy since their paper was written much earlier than the one by Srednicki.
There are some typos: "wodered" instead of wondered, and "an hole" and "an handle" which (I believe) should be replaced by "a hole" and "a handle". Also the numbers of the referred equations would have to be separated from the previous words.
One could add two things:
- a one or two line statement about how exactly string theory gets the entropy correct
- when referring to Wald's work, the statement of his main result could be added: `Entropy is the Noether charge for diffeomorphism symmetry'
Reply to Reviewer A: Thank you. I have incorporated your suggestion for how to summarize the Wald definition.
I cannot imagine how to explain in two sentences how brane counting leads to the exact black hole entropy. That is why I cite the pioneering Strominger and Vafa paper. Whoever is really interested might figure it out from reading a couple of pages of this reference.
Reply to Refviewer B: Thank you. I have fixed the typos. Also I repeated the citation of Bombelli et al. as you suggested.
My statement after Eq(12) was indeed misleading. But your suggested fix is not correct. In the classical limit the GSL is not equivalent to the area theorem. The later says the area must increase but does say by how much. The GSL stipulates a lower bound on this increase. So I have replaced the sentence right after Eq(12) by one which leads right into the two following paragraphs, and they explain the exact relationship.
Reply to Reviewer C: In the line you mention I am just citing the result of the CLASSICAL area theorem from 1971. The elaboration you suggest is already included in the article 3 lines after equation (12).