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.)