What happens if I put one pole of a magnet beyond the horizon of a black hole? Let's assume I could lower a bar magnet slowly from some position outside of the Schwarzschild horizon. What happens if it crosses the horizon, so that one pole of the magnet is inside the black hole horizon and one side is still outside? Would the outside observer then see a magnetic monopole, because the inside pole becomes "disconnected" from the outside pole? Or would the outside observer basically see one pole sit on the horizon and the other pole/end of the magnet coming closer and closer to it until it vanishes completely behind the horizon? 
 A: Gravity isn't consistent across the length of the magnet. It results in 'tidal forces', because the further away you get from the centre of a mass, the weaker the gravitational attraction. For example, for the Earth-Moon system, whilst the force involved is not very large, the Earth is big enough for this differential between the force experienced on opposite sides of the Earth in the line of the Moon to matter, and this leads to the tides, hence the name tidal forces.
Now, a typical everyday bar magnet is much smaller than the Earth; however, the gravitational attraction due to a black hole is so much larger because the density of mass involved. This means that even the small length of a bar magnet would start to experience huge tidal forces as you got closer and closer to the Schwarzschild radius, as space-time is becoming more and more warped.
Note that at the Schwarzschild radius, the escape velocity becomes greater than the speed of light itself. This means nothing can overcome the attraction. Therefore, by this point or probably earlier, your magnet will have stretched and then snapped into two parts, then snapped into more (the name for this is "spaghettification" btw, great word there), until all of the bonds will break and a stream of particles enters the black hole's event horizon.
So as one of the commenters above pointed out, it's like when you saw a magnet in half here on Earth - you get two dipole magnets, not two monopoles.
A: To add to the answer of ajd138, things are even more complicated. The point of no return around a black hole is not the event horizon, but the photon sphere that is 50% wider.
Anything between the photon sphere and event horizon must fall - only rocket engines can hold a spaceship on an orbit. However, from the standpoint of a free falling observer, the event horizon becomes smaller and smaller along the flight, so the observer, from his standpoint while falling, never crosses the event horizon until he hits the singularity.
On the other hand, if we look at this this from afar, we notice that the observer is moving slower and slower, as his time slows down while he approaches the event horizon from our viewpoint. Eventually we se heem frozen at the event horizon without crossing it ever.
As you can see, neither we nor the falling observer ever sees anything actually crossing the event horizon, such as a half of a magnet. However, even if hypothetically this were possible, cutting a magnet in half would only create two magnets.
