In Newtonian mechanics, if we throw an object in against direction of gravity with speed $v$ and it achieve max height of $h$. Now if we allow object to fall from that height $h$, it will eventually attain speed $v$ when it reach position where we launch it.
Now applying same idea to a black hole in general relativity. Speed require to escape black hole gravity is greater than $c$, so if we throw something into black hole with almost the speed of light, the object speed will exceed speed of light $c$ before hitting black hole surface! How relativity explain this? Can space-time curvature reduce speed of this freely falling object from attaining speed of light?
Answer
To answer your question you need to be clear what coordinates you're using. If you use coordinates that are co-moving with the rock falling into the black hole then the rock will see the event horizon pass at the speed of light.
External observers, using Schwarzchild coordinates, will see the rock slow down as it approaches the horizon, and if you wait an infinite time you'll see it stop.
External observers obviously can't comment on the speed of the rock after it has passed the event horizon because it takes longer than an infinite time to get there. If you use the rock co-moving coordinates then you can ask what speed you hit the singularity and ... actually I'm not sure what the answer is. I'll have to go away and think about it.
Incidentally http://jila.colorado.edu/~ajsh/insidebh/schw.html is a fun site describing what happens when you fall into a black hole.
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