I could've sworn I've seen this question before, but I couldn't find it.
Suppose I have an object on the end of a really long string. I can slowly lower it near the event horizon of a black hole, then pull it back out. But if I lower it just below the event horizon, I can't pull it back out.
This is weird, because nothing singular appears to happen at the event horizon. By the equivalence principle, the object can't detect anything different happening. And if you actually calculate the force needed to hold the object in place, it's perfectly finite at $r = 2GM$, so the person pulling from far away doesn't detect anything different either. So what makes the just-above-event-horizon and just-below-event-horizon scenarios different? What happens if you try to pull the object out?
My suspicion is that, for the second case, your pull will never be transmitted to the object: even if the tension in the rope propagates at the speed of light, it can't catch up to the mass. So the object never feels your pull at all, and you just keep pulling slack rope.
Answer
There is a treatment of lowering a string through a Rindler horizon here, (which contains a brief discussion on the extent to which the approximation is representative).
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