observers - If nothing ever falls into a black hole, why is there a puzzle about information?

From an outside perspective, nothing can ever pass the event horizon. It just scooches asymptotically close to the event horizon.

So (from our perspective on earth), when a black hole reduces in mass, is recovering the information just as simple as scooching the same material back away from the event horizon?

Answer

You can't "scootch the material from the event horizon" because in the coordinates of anything approaching the hole, the matter does in fact fall in. However, you could study for example radiation from the matter.

This is thought not to resolve the paradox for several reasons (note I gave a very similar answer to Can the event horizon save conservation laws for black holes?. I think this is an appropriate answer to both.):

1. 
   

   Real matter is quantized. The exponential redshift thus eventually leads to a sitatuation where there is a "last quantum" to fall into the hole. Eventually, it does fall in, and the matter is truly gone.

   
   
   


2. 
   

   The hole will eventually decay into Hawking radiation. Once this process is complete the infalling matter will be truly gone, replaced entirely by Hawking emission, even according to the distant observers. But the Hawking radiation doesn't seem to be entirely determined by the matter, so information seems to be lost. We know the information is not in fact lost because the black hole is mathematically equivalent to a certain conformal field theory, which preserves information by construction. Hence the paradox.

   
   

One might then offer the following also-standard response to objection 2:

This objection shows only that something strange must be happening during the actual destruction of the hole. But this is obviously a quantum gravity effect. Thus there is no need to modify our understanding of what happens to the information before the decay: it just stays painted on the horizon until the hole is destroyed.

Some canonical responses are:

3. 
   
   

   Remants seem absurd. If this response were taken seriously, it would essentially imply that all the information about the black hole - an object of potentially arbitrary mass! - can somehow be contained within a Planck-scale volume. This would be very odd.

   
   


4. 
   

   Page timescale. It can be shown that about the first half of the black-hole information must be emitted over the same "Page" timescale as it takes to emit about half of the mass. This seems to imply that something poorly-understood is going on even while the hole is large.