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.

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    $\begingroup$ The normalized surface gravity may be finite, but the speed of sound in your fishing line goes to zero, reducing the max. tension that it can withstand also to zero. If your line has infinite elasticity, then you would, indeed, pull it ever longer. If it doesn't, it will break somewhere. $\endgroup$ – CuriousOne Apr 27 '16 at 6:24
  • $\begingroup$ Related: physics.stackexchange.com/q/104474/2451 and links therein. $\endgroup$ – Qmechanic Apr 27 '16 at 9:11
  • $\begingroup$ "so the person pulling from far away doesn't detect anything different either" - but it also true that the proper acceleration of the dangling object hovering above the horizon is unbounded as $r \rightarrow 2GM$. $\endgroup$ – Alfred Centauri Apr 27 '16 at 11:21
  • $\begingroup$ "But if I lower it just below the event horizon" - you can't observe the object crossing the horizon. $\endgroup$ – Alfred Centauri Apr 27 '16 at 11:23

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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    $\begingroup$ Aha! This was the place I saw this problem, I just forgot it was a Rindler horizon. Thanks! $\endgroup$ – knzhou Apr 28 '16 at 19:23

Once a part of your string touches the event horizon you can no longer say you are lowering it because you have lost control over that matter. The only connection then remaining between you and the "string" below the horizon is causal entanglement.

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