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...Anyway: Here's my question. This is quite a headache for me, wondering how to differ one of those frames from another, I mean, a cubic mm of 'normal matter' on Earth, how many different 'frames' does it contain? it have quarks, electrons, atoms etc, all having their own mass, spins and gravity, shouldn't they too represent different 'frames of reference'? As well as a cubic mm of the event horizon (ahem:) or a black hole would do?
You can't have read the paper? The link didn't work, as I found out just now, checking it after reading your conclusions. Which bothers me quite a bit, although I have fixed it now It's quoted verbatim from "No Way Back: Maximizing survival time below the Schwarzschild event horizon." above Farsight, as I also stated in that other post. Please read it before first though, then you can always correct the authors and tell them where they did go wrong. I'm sure they will take notice, and even thank you, if you now would be correct in your conclusions. You can find them at the School of Physics at the University of Sydney. Geraint F. Lewis and Juliana Kwan.
As for the rest? Well, we seem to differ in our view of the importance of those frames of reference. I find those frames to be more than just abstractions, they are closer to reality than anything we had before them...
You wrote "As the infalling observer gets closer to the event horizon his proper time is increasingly time dilated. At the event horizon this time dilation is infinite. So that finite proper time is being measured using a stopped clock! All processes are similarly stopped. Hence: " Well, that's one view, but as far as I understand 'frames of reference' your wristwatch will 'tick' as usual when compared against the rate of your heartbeats, no matter (excuse the pun) where you are. If infalling towards the EV, or being here on Earth. To assume otherwise means that you disallow both Eddington and Finkelstein.
Also, the time dilation can only be proved versus a common origin as in the twin experiment where you know before that they were identical twins, even though it is valid for all other frames too naturally. And that we already have tested, and found to be correct. For example, GPS systems have to be adjusted for different frames of reference. And as for Einstein doubting it. He didn't protest because he thought of any 'clocks stopping' as you seem to assume.
"Einstein himself wrongly thought that black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius... In 1939 he published a paper that argues that a star collapsing would spin faster and faster, spinning at the speed of light with infinite energy well before the point where it is about to collapse into a black hole. This paper received no citations, and the conclusions are well understood to be wrong. Einstein's argument itself is inconclusive, since he only shows that stable spinning objects have to spin faster and faster to stay stable before the point where they collapse.
But it is well understood today (and was understood well by some even then) that collapse cannot happen through stationary states the way Einstein imagined. Nevertheless, the extent to which the models of black holes in classical general relativity correspond to physical reality remains unclear, and in particular the implications of the central singularity implicit in these models are still not understood. Efforts to conclusively prove the existence of event horizons have still not been successful, and most scientists acknowledge that no such proof is even possible.
To expect a frame of reference existing in SpaceTime where 'times arrow' won't 'tick/move' is interesting but, as I expect it to be, wrong. You have to differ between the frames of reference. That the far observer sees the infalling observer 'hover', unmoving above the event horizon, is a direct result of two 'frames of reference' not agreeing on time, nor distance.
We have to assume that times arrow exists inside a event horizon too. To do otherwise should mean that matter would have no time-like direction after meeting the event horizon, and if so I expect the matter unlikely to pass the EV, even though that clock still was ticking to your heartbeats, all the way down to it. That seems, to me, to indicate that the singularity would be hidden inside a surface of matter, resting on the Event Horizon, which I deem highly improbable.