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Falling freely into a black hole (assuming we survive or being point-sized) all particles in front of you are accelerating away from you in the direction of the singularity which seems flying towards you. It only takes a small amount of time to reach the center, about the time it takes light to cross a Schwarzschild radius distance, which in the case of the Sun is about 1/100000 seconds.

Still it seems that you can never reach a particle that falls in front of you as it keeps on moving away from you while falling.

Meanwhile in the universe outside the hole it seems you are stuck on the horizon and in the little proper time that has passed on your watch, the coordinate in the universe has run on speed, so to speak.

I'm a bit confused how things in the hole end up. Do the particles end up stretched in space and time? Is the hole maybe evaporated (the evaporation radiation, or Hawking radiation, taking away your last state of being) before you end up anywhere?

EDIT

Let me phrase the question differently. You start falling freely in a region where the hole's gravity is weak (so it doesn't take an infinite time to fall in. Along the radial distance in your freely falling falling frame that accompanies you, you place poni-like masses with equal distance between them. On the back of these masses we have put point-like clocks (which sounds a bit odd but they are not affected by tidal forces).

So what will happen to the distances between the masses and what will the clocks show, relative to the others and a clock at infinity? It seems to me that the distances between the masses grows without limit while the proper clocktimes will differ too but not more than the time it takes for light to cover a Schwarzschild radius (which is about 1/100000 seconds for a hole with the mass of the Sun).

So, can we say that all matter involved of the formation of the hole is stretched out infinitely in the radial direction while the entire time it seems to take for a faraway observer at rest (which can be a very long time) is projected to a small time interval in the falling frame?

Gerald
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  • Everything ends up at the singularity in a finite proper time. Where do you get the idea of particles being "stretched in space and time"? There are no non-speculative ideas for what happens at the singularity. – ProfRob Aug 20 '22 at 14:00
  • @safesphere When you fall in all particles in front of you accelerate away from you. In your local frame falling with you the particles initially at rest in infinity accelerate away from you. And the clocks on the backs of these particles tick differently relative to one another. You look at the situation from the coordinate time. – Gerald Aug 20 '22 at 15:39
  • @ProfRob Imagine you start falling at infinity. Particles ligned up radially with equal distances. The particles start accelerating away from each other and the clocks on their backs start showing differences. So inside the hole as "seen" when falling along they end up with a lot of space between then radially and with some time differences. The whole universe time seems to fit in the proper time inside the hole. Maybe the hole evaporates before all matter ever has fallen in. – Gerald Aug 20 '22 at 15:46
  • @ProfRob If you compare clocks inside with clocks far away the faraway clocks seem on speed. It takes the proper time to reach the end but the singularity is not a point. – Gerald Aug 20 '22 at 15:48
  • Who is "you"? An infalling observer does not see "speeded up" clocks in the distant universe. – ProfRob Aug 20 '22 at 15:55
  • @safesphere Why not? The whole history if the hole can be projected on the infinite line and (say) ten million years in a small proper time. – Gerald Aug 20 '22 at 16:13
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    An infalling observer can indeed compare their clock with distant clocks both outside and inside the event horizon up to the proper time at which they reach the singularity. The stuff about reversal of space and time axes is irrelevant and has no bearing on what a falling observer would measure. As the ticks on their clock continue they will reach smaller and smaller radial coordinate. You should read the answers to https://physics.stackexchange.com/questions/82678/does-someone-falling-into-a-black-hole-see-the-end-of-the-universe?rq=1 – ProfRob Aug 20 '22 at 16:33
  • @safesphere It's still unclear to me. Can't we say that the whole history of the hole is prkjected onto an infinite line, the times along it varrying just a small interval of time? I still can't see the time-radialspace change takes place in the falling frame. From the outside the hole matter seems to end up at the horizon sphere (the hole never actually forming, while in the falling frame the whole history ends up stretched out infinitely in radial space direction each point corresponding to different times but no clocks showing more difference than the proper fall time. – Gerald Aug 20 '22 at 21:37
  • @safesphere you are wrong and yet again just add confusion to what is possibly a straightforward question. In-falling observers can receive signals (clock ticks) from external observers right up until the point they reach the singularity. No sensible person uses Schwarzschild coordinates to deal with events straddling the event horizon. – ProfRob Aug 20 '22 at 21:42
  • @ProfRob Yes, that's what I think too. Why should time and space be interchanged in the falling frame? What does that mean? – Gerald Aug 20 '22 at 21:53

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