Or it pauses in time because the spaceship reaches the speed of light, c?
There is a powerful time dilation element to what is seen by a distant observer, and the falling object appears to grow every slower (as well as ever more red shifted) as it approaches the event horizon. Asymptotically so, such that (if you are observing on a long enough wavelength) the falling object never quite vanishes.
The example that I saw given by Leonard Susskind as described in the book 'The Black Hole War' depicted two characters, Bob and Alice, flying aimlessly in the immediate vicinity of a Black Hole (as you do).
It explains that if Alice were to jump out and float towards the Black Hole, Bob would see her slowly reaching the Event Horizon before becoming totally 'static' and fixed, Alice's point of view however would see her passing into the Black Hole before ultimately meeting her rather unfortunate end - suggesting that this provides a 'hologram' effect.
There are other such descriptions around Black Holes such as the propeller multiplication suggestion also made by Susskind - which suggests that propellers on an Aeroplane would continuously multiply upon reaching the vicinity of the Black Hole.
Either way, the book is worth checking out - I'm no scientist myself (and it probably shows), I just happen to have a passing interest.
Hope this helps.
truth the answer is a little more complicated. suppose we have a spacecraft orbiting a black hole. This falls on the first bias that we have regarding this type of object: unless we're very close range to the black hole, gravity they generate is identical to that generated by a star having the same mass. As a spacecraft can orbit around it the same way it does around the Earth.
For example, if we we replaced the sun by a black hole with the same mass as the Sun, Earth would not notice absolutely no difference, so our orbit would remain the same, without undergoing any change.
Now our ship spacing is mounted on a probe, leaving the main hall that continues to orbit the black hole, and begins to descend into the hole. As it descends, is throwing light signals (say, blue) to the ship, so that these light signals can continue his career.
At the beginning of its descent, not detected any unusual symptoms. It is analogous to any previous decline has made any astronaut to Earth.
However, as it approaches the black hole, one begins to notice some differences: gravity varies more quickly, which causes the gravity you feel the front of the spacecraft is slightly different from that sit in the back.
This effect is more noticeable the closer the "hole" and the smaller it because for the supermassive (like the one in the center of galaxies) is much larger size, thereby reducing variation in this intense gravity.
Following his fall, and looking up, we see that the whole sky is "deformed" by concentrating on the point opposite where the black hole. This is because the intense curvature which occurs on the light path of gravity of the hole.
When the spacecraft approaches the event horizon it is increasingly noticing a difference of greater severity, it keeps the "sky" more focused on the point opposite the center of the black hole and a color more and more "blue".
While watching, he notes that, things start to happen faster and faster (everything seems to move at a faster rate). Here is another consequence of a gravitational field so intense: the time begins to run much slower, so for him is the rest of the Universe who is going much faster.
Finally, when crossing the event horizon, our spacecraft will not see absolutely nothing, but continue to monitor the same as for a moment before entering.