Nothing.
There is only one reference frame where the proper physics occurs and that is the one that you are in as you fall into the black hole. You would be freely falling into the black hole, and from this reference frame nothing unusual happens at the horizon. General relativity says that at the event horizon as seen by you, nothing unusual is going on at all. All you would be feeling are the tremendous tidal forces of the black hole, and these could be very substantial across a distance equal to your arm's length. In fact for a stellar-sized black hole, even before you got to the horizon, the difference in the gravitational pull between your chest and hand is a factor of several hundred, so that your hand would be torn from your body. But by then that will be the least of your problems.
Distant observers, in principle, would see your hand 'wink out' followed moments later by the rest of you!
Copyright (C) 1997 Dr. Sten Odenwald
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