In "Entropy in Black Hole Pair Production" (arXiv:gr-qc/9306023), Strominger et al. notes

The issue of whether (1.2) can be taken literally has bearing on the vexing question of what happens to information cast into a black hole. If one assumes that (1.2) counts all the black hole states, and that information is preserved, then one is forced to conclude that information escapes from a black hole at a rapid rate (proportional to the rate of area decrease) during the Hawking process. We do not think this is likely because it seems to requires a breakdown of semiclassical methods for arbitrarily large black holes and at arbitrarily weak curvatures, although this point is certainly the subject of heated debates!

Here $(1.2)$ is $$N=e^{S_{bh}} \tag{1.2}$$ where $S_{bh}$ is the black hole entropy.

  1. How do we conclude that the information escapes at a rate proportional to the area? We have, $N=e^{S_{bh}}$. Therefore, I get:

    $\dfrac{dN}{dt}=e^{S_{bh}}\dfrac{dS_{bh}}{dt}=e^{S_{bh}}\dfrac{dA}{4dt} {\sim} e^{S_{bh}}\dfrac{dM^2}{dt}{\sim}e^{S_{bh}}r\big(r^2T^4\big){\sim}e^{S_{bh}}r^3\bigg(\dfrac{1}{r^4}\bigg){\sim}\dfrac{e^{A/4}}{\sqrt{A}}$

  2. If I figure out how the information evaporation rate is proportional to the area then how do I make sense of it requiring breakdown of semi-classical methods for arbitrarily large black holes and arbitrarily weak curvatures?

It seems to me that since they say that such a condition requires breakdown of semiclassical results for arbitrarily large black holes, the semiclassical treatment I used in Point 1 isn't something they are using to claim what they are claiming. They are using something different. But they haven't linked any reference as to in which context they are claiming this. Maybe I am naive and am unfamiliar with some basic results of blackhole thermodynamics that they are using to claim this. Kindly suggest how to understand the two points mentioned above.


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