What happens to matter falling into a black hole?

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Matter falling into a black hole does not exceed the speed of light but approaches it as it nears the event horizon. Once past the event horizon, defining velocities becomes ambiguous due to the absence of stationary observers. In-falling objects continue moving toward the singularity, rather than stopping. Remote observers perceive these objects as slowing down and appearing to 'freeze' due to gravitational redshift. The behavior of matter in black holes remains a complex topic in relativity.
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Does the gravitational force of black holes pull matter in at speeds faster than the speed of light? (when the matter has passed the event horizon that is?)

Or does the matter just stop moving out and in? and stop where it is?

Or do we not know anything about this just yet... which I'm assuming
 
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As in all relativity, when you speak of velocities you must specify with respect to whom you are measuring these velocities. For example, with respect to shell observers, in-falling objects approach the speed of light as they approach the event horizon. Since there are no stationary observers within the EH, defining velocities becomes even more ambiguous. Matter certainly doesn't stop, it is destined to end up at the singularity.
 
Nabeshin is correct. Weirdly enough, remote observers perceive that objects falling into a black hole slow and eventually 'freeze' as they approach the event horizon due to gravitational redshift.
 

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