> But the object passing the event horizon passes through just fine.

Yes, but due to the extreme time dilation, will they observe/experience the heat death of the universe prior to entering the black hole?

If so, does it make sense to say they actually enter it in any meaning full sense from the perspective of our existence?

As in 'yes', they will enter the black hole, but they will enter it an infinite number of years from now when our universe "functionally" no longer exists.

Isn't this just another form of a particle with constant acceleration, accelerating to the speed of light? Yes, from their perspective, they reach it, but from our perspective, it will take an infinite amount of time and so we say they never can reach it from either our perspective or theirs? I don't see how this can be any different. Gravity is a constant accelerator.

(And note I'm calling out the constant acceleration case above for approaching 'C', not the increasing acceleration requiring 'exponentially increasing energy each second' case).

Consider this argument: if you can see the person falling in for "infinitely long", then you can actually communicate with this person falling in. For example, through light or gestures. Since you can communicate, this means the image you see of the person falling in is not just an illusion or artifact of general relativity, you both must agree on reality, that the person still hasn't crossed the horizon.

Nope, your signals also slow down and never reach them, and they appear to be 'frozen' and cannot respond to you. As they approach the event horizon their "reflexes" slow down in a kind of Zeno's paradox. Your signals never reach the infalling observer, so you cannot communicate. And they have a finite amount of reaction time as they fall through the black hole, but to your perspective that gets smeared over an infinite amount of time in the future. This is only due to the fact that you both disagree over how to measure space and time at the event horizon. To the infalling observer this isn't of any consequence though since all actual physics is local and your ruler and stopwatches aren't relevant to the infalling observer.

If their light reaches you, your light could reach them, this is a reciprocity condition that I believe is valid in GR too (because effectively light follows null geodesics, and it can always go both ways, geodesics don't have a preferred direction).

It's true that infalling observers will experience outside time speeding up, and conversely outside observers will see infalling objects slow down. In fact, as they approach the Event Horizon, they would appear to experience diverging time dilation. So in effect, they become "frozen in time". But remember that you can always maintain two-way communication with light. The very fact that both the outside observer can always see the infalling person and the infalling person can always see the outside world imply there can be two-way communication all the way up to crossing the event horizon (which would take infinitely long for the outside observer). This ought to be enough to conclude the infalling person can in fact never reach the event horizon.

> It's true that infalling observers will experience outside time speeding up, and conversely outside observers will see infalling objects slow down.

And the infinite passage of all external time is observed in a finite time by the infalling observer. All of the communication from the external observer is going to become a high frequency chirp at the event horizon, and the last message the infalling observer could send will take nearly an infinite amount of time to reach the external observer. And in the next instant of subjective time by the infalling observer they will be past the event horizon and unable to communicate any more.

Sure, but it seems this is unphysical if this passage occurs after essentially an infinite time for an outside observer. Before crossing the event horizon, the infalling person sees the whole history of the universe. But the problem is, if crossing the horizon takes infinitely long, how could the horizon form in the first place? That's what I've never seen addressed to a satisfactory degree.

Well elsewhere in this thread I've pointed out that the black hole evaporates before the infalling observer ever crosses the event horizon.

If you have a classical black hole and you don't bother yourself with how it forms, though, there's no paradox, the paradoxical effects arise because the areas of space-time become completely unreachable and you're using coordinate systems which are not local.

Yeah, you're right. It's not an optical illusion. I think I'm wrong about the infinite acceleration part though. We never observe the person hitting the event horizon so time never actually freezes. It just gets really really slow and approaches the point of time freezing.

The person falling into the black hole will have time in the outside universe accelerate relative to him. It will get faster and faster and when he hits the event horizon we don't know what happens as that's the singularity where the math no longer works. We can speculate that time actually freezes but that leads to paradoxes.

No you're wrong. It's not just some optical illusion. It's a seemingly paradoxical statement.

From the perspective of the observer nothing enters the black hole. This is true.

From the perspective of the person entering the black hole he does enter it. It's because of time dilation.

Both of these statements are true according to theory as far as I know.

But then on a long enough timescale the black hole evaporates via hawking radiation in a finite amount of time before the external observer has ever seen the 'frozen' object fall through the event horizon.