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If an object falls into a Schwarzschild black hole and a distant observer watches, they see the object fall slower and slower as it approaches the event horizon, until it is "frozen." (To the observer, it never stops accelerating.) The observer never sees the object cross the event horizon in finite time.

So, with this, how is information about the object lost? Shouldn't the observer have the ability to observe the object indefinitely? To them, shouldn't the object appear "on this side" of the universe indefinitely? Shouldn't the object's light, mass, and charge remain observable "on this side?"

Question: Where does information loss in this setup occur, i.e., which aspects about the object are lost; and—if it makes sense to ask such a thing—when does it occur, i.e., when (with respect to the observer) during the object's approach does the observer lose the ability to measure all of the information about the object?

(If the two questions are not related enough to be asked at the same time, please let me know so I can break this up into multiple questions, Thanks.)

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    $\begingroup$ I asked myself this question for a few years now, and haven’t found an answer. $\endgroup$
    – Andrea
    Commented Oct 1, 2019 at 16:04
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    $\begingroup$ Stuff falling into a BH emits a finite amount of light before it crosses the event horizon, so for a distant observer it doesn't just get red-shifted, it rapidly gets too dark to see, as described here. $\endgroup$
    – PM 2Ring
    Commented Oct 1, 2019 at 16:41
  • $\begingroup$ @PM2Ring Good point, thanks! $\endgroup$
    – BMF
    Commented Oct 1, 2019 at 16:43
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    $\begingroup$ The black hole information paradox does not come from classical general relativity. It's tied to Hawking radiation. Black holes are expected to evaporate because of Hawking radiation, and that is central to the information paradox $\endgroup$
    – Chiral Anomaly
    Commented Oct 1, 2019 at 17:59
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    $\begingroup$ Possible duplicate of Why is information "lost" when it got into a black hole? $\endgroup$
    – A.V.S.
    Commented Oct 1, 2019 at 18:11

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In the proper time of the object falling into the black hole, it crosses the event horizon and hits the singularity in finite time. But the observer outside 'sees' the object never reaching the event horizon. So, for the observer, the object never reached the event horizon. Whatever the observer sees, are events that happened before the object crossed the horizon. Hence the information on what happened to the object after it crossed the horizon is lost to the observer.

Edit: In classical black holes there is no information loss. When the black hole evaporates following thermal Hawking radiation there is no way to retrieve the information of the particle that falls into the black hole. That is to say there is no unitary transformation which can trace back to the state of the particle prior to it hitting the singularity.

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  • $\begingroup$ Ah! Is that my mistake? We don't lose the information about the object's approach, but its activities afterwards. Huh, in retrospect, that should've been obvious. I guess my thinking was that we couldn't get any information about objects that entered the black hole prior. That information was "lost," while to me it seemed that that information just accumulated around the black hole, albeit, very redshifted. $\endgroup$
    – BMF
    Commented Oct 1, 2019 at 16:02
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    $\begingroup$ Yes, you lose the information after the object falls into the black hole. The first paragraph of this page: en.wikipedia.org/wiki/Black_hole_information_paradox may be helpful for the basic understanding. $\endgroup$
    – abhijit975
    Commented Oct 1, 2019 at 16:24
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    $\begingroup$ It seems that your notion of simultaneity is not correct. You must differentiate 1) what an outside observer sees and 2) what is simultaneous from the point of view of an outside observer, see my answer to this question. $\endgroup$
    – Moonraker
    Commented Oct 1, 2019 at 19:22
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    $\begingroup$ That means that the infalling observer will cross the event horizon only at the end of time of the outside observer such that, from the point of view of an outside observer, the information is always available, and this until the end of time. - That means that the question has not been answered. See also my question which still has not been answered. $\endgroup$
    – Moonraker
    Commented Oct 1, 2019 at 19:23
  • $\begingroup$ What I mean to say is once the particle enters into the black hole and the black hole eventually evaporates due to thermal Hawking radiation, there is no way to retrieve the lost information $\endgroup$
    – abhijit975
    Commented Oct 1, 2019 at 20:55

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