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Well, this is by no means settled, but that's ok (meaning any answer is likely going to be seen as controversial until further observation provides more data).

Well, this is by no means settled, but that's ok (meaning any answer is likely going to be seen as controversial until further observation provide more data).

Matter whose rate of energy absorption/energy emission is said to be effectively zero is recognized to be Bose-Einstein condensate - which raises a question about the nature of the event-horizon. Paul R. Anderson, Roberto Balbinot, Alessandro Fabbri, Renaud Parentani and others have shown (Hawking radiation correlations in Bose Einstein condensates using quantum field theory in curved space) that a Bose-Einstein event horizon will produce Hawking radiation, and this has been observed (Hawking radiation in a two-component Bose-Einstein condensate, P.-É. Larré, N. Pavloff)

Matter whose energy content, whose rate of energy energy emission said to be effectively zero is recognized to be Bose-Einstein condensate - which raises a question about the nature of the event-horizon. Paul R. Anderson, Roberto Balbinot, Alessandro Fabbri, Renaud Parentani and others have shown (Hawking radiation correlations in Bose Einstein condensates using quantum field theory in curved space) that a Bose-Einstein event horizon will produce Hawking radiation, and this has been observed (Hawking radiation in a two-component Bose-Einstein condensate, P.-É. Larré, N. Pavloff)

Consider, as your falling clock falls toward an event horizon it gains speed, and loses thermal energy (else poses problems for the black-hole due to the 2nd law of thermodynamics). As it falls more quickly, because its time slows, the rate at which it loses energy will appear to decrease. It will appear to go the speed of light at the event-horizon but never appear to cross over because of its stopped time. It should also not have any energy. Because black-holes are not thought to break the 2nd law of thermodynamics it is generally believed necessary that all energy is radiated away through thermal or Hawking radiation before the event Horizon is reached, but for the sake of your question lets suppose this doesn't matter. The point is that once it reaches the event-horizon the rate of energy loss must appear to be zero for, as you point out, this clock's time period compared to the remote clock observing, will be infinitely long.

It also means that the falling clock is still available to interact with an observer clock a billion years from now, that it is not truly "in the black" but to do so would require it to be able to absorb energy. The property of Bose-Einstein condensate with respect to Hawking radiation has been studied, both near and on the event-horizon itself, and although it is not impossible for this to happen, it is not very likely.

Consider, as your falling clock falls toward an event horizon it gains speed, and loses thermal energy (else poses problems for the black-hole due to the 2nd law of thermodynamics). As it falls more quickly, because its time slows, the rate at which it loses energy will appear to decrease. It will appear to go the speed of light at the event-horizon but never appear to cross over, or go faster, because its time appears stopped. It should also not have any energy. Because black-holes are not thought to break the 2nd law of thermodynamics it is generally believed necessary that all energy is radiated away through thermal or Hawking radiation before the event Horizon is reached, but for the sake of your question lets suppose this doesn't matter. The point is that once it reaches the event-horizon the rate of energy loss must appear to be zero for, as you point out, this clock's time period compared to the remote clock observing, will be infinitely long.

It also means that the falling clock is still available to interact with an observer clock a billion years from now, that it is not truly "in the black" but to do so would require it to be able to absorb energy. The property of Bose-Einstein condensate with respect to Hawking radiation has been studied, both near and on the event-horizon itself, and although it is not impossible for this to happen, it is not very likely. Matter near but not touching a Bose-Einstein event-horizon can still radiate away energy, but matter in physical contact with it must become part of the event-horizon itself (which is fascinating too because Bose-Einstein event-horizons have also been shown to have fractal dimensions)