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There are many questions on this site about whether you can really fall into a black hole - some seem to say clearly yes, some say clearly no. So let's try one more stab at this one with a narrower question:

If you drop a large number of sodium ions into a black hole, and you live a really long time and from many angles dutifully watch the emissions from the sodium ions and the absorption of the Hawking radiation by the sodium ions once it gets bright enough near the end, is there ever any time (right up until the evaporation of the hole) when the sodium ions are not in front of (at a greater radius than the source of) the Hawking radiation?

Some presumptions here: (a) you never stop receiving photons from anything dropped in a hole, and (b) the Hawking radiation originates right at the event horizon. Please feel free to dispute these.

Mike Serfas
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  • Classically, nothing that originates "at" the event horizon can ever get out to infinity, simply because the event horizon is defined to be the set of points for which no causal worldlines can reach (null) infinity. So your premise (b) is problematic at best. – Michael Seifert Feb 23 '21 at 15:11
  • That said, I couldn't tell you how this changes in the quantum picture, other than waving my hands and mumbling something about the Heisenberg uncertainty principle. In particular, I'm not sure what you can really say about the "point of origin" of Hawking radiation, or whether you can say anything meaningful at all. – Michael Seifert Feb 23 '21 at 15:11
  • @safesphere: "No" is a perfectly acceptable answer - I hope that makes the question less problematic. :) You make interesting points, but (a) is the Planck length you measure a distance that the infalling particle actually sees, or is it perpendicular to the spacetime the particle moves in? (b) If you are dropped 1 AU from a black hole and begin falling directly toward it, when do you see the Hawking radiation disappear? – Mike Serfas Feb 24 '21 at 21:11

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