# Black hole complementarity - absorption of Hawking radiation

I try to understand two principles formulated by Leonard Susskind in his book The Black Hole War:

1, To any observer who remains outside a black hole, the stretched horizon appears to be a hot layer of horizon-atoms that absorb, scramble, and eventually emit (in the form of Hawking radiation) every bit of information that falls onto the black hole.

2, To a freely falling observer, the horizon appears to be absolutely empty space. [...]

Now, in reaction to (an unanswered) question by Nathaniel, let us suppose that a distant observer A sees (according to the principle #1) Hawking radiation from a black hole (with Planck spectrum and say measurable temperature). Now suppose there is a freely falling gas somewhere between the event horizon and the observer. According to the principle #2, to the gas (considered an observer B) the horizon is empty space so there is no light coming from it to absorp.

Would the observer A detect absorption lines in the black hole spectrum? How does it change with distance of the gas (or the observer) from the black hole? Will the distant observer see the lines if he is free falling?

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My point of view : The infalling matter, which could be the original matter which build the black hole, or additional matter as your gas, only contibute to increase the total mass of the black hole, and so modify (decrease) the temperature of the black hole. So, by this indirect way, there is a relation between your gas and the Hawking radiation, but there is no direct interaction between the gas and the Hawking radiation. – Trimok Oct 10 '13 at 9:46
@Trimok The gas is outside the black hole, and doesn't contribute to its mass no more than the observer A does. – Leos Ondra Oct 11 '13 at 12:21
For the outside fixed observer $A$, there is no black hole interior, there is only a horizon. What I mean is, more the gas goes next to the horizon (from the point of view of $A$), more it appears like being part of the "horizon/ black-hole", so, at the limit, the gas will increase the mass of the black hole. Of course, the observer $A$ does not. – Trimok Oct 11 '13 at 17:16
And note that any answer will have to repeat this question for the case of Unruh radiation. – Jerry Schirmer Dec 14 '13 at 21:41

Your point #1 has to do with the fact that some physicists believe that if information did not RETURN, it would violate the Unitary principle. The philosophy of Quantum Mechanics demands that Unitary is immutable. Therefore some people had come up with theories to show that information is not really lost in the blackhole.

I have not read the book you mention, but I happen to be reading The Rode to Reality from Penrose, and there is a section in the book where he actually touches on this same subject. However, I am afraid that Penrose, does not share this view, in effect in relation to your Point #1. To quote him (page 841), "I find it inconceivable that somehow 'at the moment just before the horizon is crossed' some sort of signal is emitted to the outside world conveying outwards the full details of all information contained in the collapsing material...Simply a signal would be by itself not be enough, since the material itself is, in a sense, really the "information" that one is concerned with. Once it has fallen through the horizon, the material is trapped, and is inevitably destroyed in the singularity itself"

Perhaps this is not the answer you were looking for, but I hope that it is of some value to you.

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First of all sorry for answering you not having a physics education.

If the gas does not fall into the black hole (there is at least a minimal distance between the event horizon and the gas molecules) the absorption would behave the same way as if the black hole was a "regular" star that has the same spectrum as the Hawking radiation.

Because of the high speed of the gas and the large masses relativistic effects must be considered.

As far as I understand the Hawking radiation's source is the empty space near the event horizon of the black hole and not the black hole itself. That theory says that in empty space photons and anti-parts with a negative (!) energy (and mass) are formed but normally these pairs will destroy themselves at once. Near a black hole the anti-parts fall into the black hole while the photons depart from the black hole. (If this is true then Nathaniel's theory is wrong - the Hawking radiation is formed when the black hole is already existing.)

This would mean that the gas between the event horizon and the point where the Hawking radiation originates does not influence the Hawking radiation (while the gas that is more distant from the black hole behaves like the gas close to a "regular" star).

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