Exploring Time and Space Dilatation Near Black Hole Event Horizon

[Roberto Pavani]

TL;DR Summary

Most physics books says that an observer falling on an huge black hole (so to have negligible tidal forces) should pass through the event horizon "harmless".
Here some thought about what he should "really" see and what then could happen to the observer.

As closer the observer will be to the event horizon, the more the time dilatation will be.
As we know, if the observer O1 has a clock, another observer O2 very far from the black hole will se the O1 clock "slowing" down
as O1 approach the event horizon. The limit is that the O1 clock "stops" at the event horizon.

But what O1 will see?
O1 will see that O2 clock is "accelerating" as O1 is approaching the event horizon. The limit is that O1 clock will go to an infinite "speed"
when O1 reach the event horizon.

O1 Observer is also looking to the galaxy that is surronunding the black hole, He will see all the stars moving around the center the galaxy (where the black hole is) moving "faster and faster" as he approach the event horizon.
Because of space dilatation (needed, otherwise he will see stars moving faster than light) those stars will be detected closer and closer to the O1 observer.
Also all far galaxy will be observed closer and closer as the observer O1 approach the event horizon.
All the incoming photons from the galaxy stars and all other galaxy will have frequency measured by O1 increasing the closer O1 is to the event horizon.
When he will be so close to the event horizon that 1s for him is 1 billion year for the galaxy stars, he will receive in just one second all the photons sent by all the stars for 1 billion year at a frequency 31.5 10^15 times the original frequency.
That should burn the observer just before reaching the event horizon.

But because of all the surrounding stars of the galaxy will be closer to him (space dilatation), would be possible that their gravitational force will change the event horizon position for the O1 observer ?

 

[.Scott]

Others can check me on this, but I don't believe that O1 will ever observe "O2 clock will go to an infinite "speed"" at the event horizon or anywhere else.

And I believe you mistyped an O1 where you meant an O2.

 

[Nugatory]

But what O1 will see?
O1 will see that O2 clock is "accelerating" as O1 is approaching the event horizon. The limit is that O1(I think you meant 'O2'?) clock will go to an infinite "speed"
when O1 reach the event horizon.

That is not what happens. The problem is that you're working with Schwarzschild coordinates, and because these have a coordinate singularity at the event horizon they don't give valid results there. Instead we need to work with something like Kruskal coordinates, which don't have this bogus singularity at the horizon.

One good explanation is https://arxiv.org/abs/0804.3619 (especially the part about why the infaller does not see the entire future of the universe), and you might also want to try the series of Insights articles on the Schwarzschild spacetime (note that's the Schwarzschild spacetime, not the just the coordinates!) here by @PeterDonis.

As this thread is based on a misunderstanding it is closed. However, you are welcome to and encouraged to start new threads as long as you are trying to understand what does happen, instead of drawing conclusions from what you think is happening.

 

[PeterDonis]

Here some thought about what he should "really" see and what then could happen to the observer.

To add one other comment about this: your statements about time dilation and the blueshift of incoming radiation apply to a static observer--an observer who is "hovering" at a fixed altitude above the hole's horizon. (Note that there cannot be any static observers at or below the horizon.) They are not valid for an infalling observer, one who is free-falling into the hole, which is the kind of observer you said you were talking about. An infalling observer O1 will see the clock of the faraway observer O2 to be running slow, not fast, and he will see incoming radiation from the rest of the universe redshifted, not blueshifted.