Of course. I’m not arguing against the different frames of reference. I’m arguing against what I interpreted – perhaps incorrectly – to be your implication that matter can never actually fall into a black hole. If that were true, singularities and black holes as we understand them could never form in the first place. But certainly the predominant scientific consensus is that it can, and they do.
This is as good an article as I’ve found trying to explain this apparent paradox. The key quote:
If we program a space probe to fall freely until reaching some randomly selected point outside the horizon and then accelerate back out along a symmetrical outward path, there is no finite limit on how far into the future the probe might return. This sometimes strikes people as paradoxical, because it implies that the in-falling probe must, in some sense, pass through all of external time before crossing the horizon, and in fact it does, if by “time” we mean the extrapolated surfaces of simultaneity for an external observer. However, those surfaces are not well-behaved in the vicinity of a black hole. It’s helpful to look at a drawing like this.
This illustrates schematically how the analytically continued surfaces of simultaneity for external observers are arranged outside the event horizon of a black hole, and how the in-falling object’s worldline crosses (intersects with) every timeslice of the outside world prior to entering a region beyond the last outside timeslice. The timeslices have the form
[INDENT]tj − T = 2m ln(r/2m − 1)
where T is the (inward) Eddington-Finkelstein time coordinate. We just repeat this same shape, shifted vertically, up to infinity. Notice that all of these infinitely many time slices curve down and approach the same asymptote on the left. To get to the “last timeslice” an object must go infinitely far in the vertical direction, but only finitely far in the horizontal (leftward) direction.
The key point is that if an object goes to the left, it crosses every single one of the analytically continued timeslice of the outside observers, all the way to their future infinity. Hence those distant observers can always regard the object as not quite reaching the event horizon (the vertical boundary on the left side of this schematic). At any one of those slices the object could, in principle, reverse course and climb back out to the outside observers, which it would reach some time between now and future infinity. However, this doesn’t mean that the object can never cross the event horizon. It simply means that its worldline is present in every one of the outside timeslices. In the direction it is traveling, those time slices are compressed infinitely close together, so the in-falling object can get through them all in finite proper time (i.e., its own local time along the worldline falling to the left in the above schematic).[/INDENT]
Another quite interesting intuitive explanation from the same site is found here. Interpreted strictly in terms of Schwarzchild coordinates, one can regard an infalling object as taking infinitely long to pass the event horizon, and then (recalling what happens to the time dimension beyond the EH in the Schwarzchild solution) traveling back in time to the present in Schwarzchild coordinate time as it progresses from the EH to the singularity, yielding a net transit time to the inevitable singularity as seen by an external observer to be not much different from its own proper time. I have no idea if this interpretation makes physical sense, but not much beyond the event horizon really does. If we launch a massive object into a black hole and very soon observe that the radius of its event horizon has grown, then something like this must be true.