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[Tylui]

What if we give the falling observer and the object-before-it a propulsion system that would exactly counteract the gravity acceleration at any moment of falling down? That would make them stationary.

If they're stationary, then they're not in-falling, no?

They can still move at a constant speed relative to the black hole and be considered a "stationary observer".

Il Pal, it seems you do have a better grasp than you think! Sergarr, if you fire the propulsion system on both objects while they're both outside, nothing strange happens. If you fire them while one is inside, and one is outside, then you encounter the exact same situation as before; once the object is inside, it CANNOT come to rest with respect to you, since it would need to travel faster than the speed of light. If you were falling in after the object, you'd see it falling in too, along with anything else that's falling in.

The most intuitive way I've found of thinking about this stuff is with Kruskal–Szekeres coordinates where any objects falling in use the regular T and X axes, and where any stationary observers use r and (little) t, in the number I quadrant. little r = 1 would be 1 unit away from the Schwarzschild radius. To better understand the I quadrant, stare at left half of this Penrose diagram...

Another thing that really helped is this youtube playlist: Topics in String Theory; lectures by Leonard Susskind. Lectures 3, 4, and 5, and maybe others deal with black holes a great deal, and really don't have that much to do with strings or quantum mechanics.

EDIT: Actually this video is basically exactly what we're talking about, with the 2 in-falling observers being explained at 1hr 0 min: General Relativity Lecture 7 It's funny we were talking about it then I decided to keep watching this one, and here it is

[hops]

I think the rate of time is like velocity. Just because objects move at difference speed, doesn't mean that velocity doesn't exist, so the same could be said with time.

Seems like I get ignored every time I say that time is a location, though. But I guess that it's kind of confusing to parse.

[Sergarr]

Il Pal, it seems you do have a better grasp than you think! Sergarr, if you fire the propulsion system on both objects while they're both outside, nothing strange happens.

So when do you observe the object ahead of you entering the black hole?

[Tylui]

If you stay on the outside, you'll never see it go through. If you go through after it, you won't see anything especially weird, apart from the weirdness your incredibly strong propulsion system might have with relativity and such, should you choose to fire it.

[Sergarr]

But if you never observe it getting into the black hole, then how can you enter the black hole yourself? You'd need to do it after the object ahead of you does it, and it essentially never does as long as you're still outside. The distance between you would shorten, but you still wouldn't be ahead of it - and thus not in the black hole. If you want cross the black horizon, you would need to essentially crash into the object ahead of you to do it.

That's why it's sorta like a Zeno's paradox.

[Tylui]

But if you never observe it getting into the black hole, then how can you enter the black hole yourself? You'd need to do it after the object ahead of you does it, and it essentially never does as long as you're still outside. The distance between you would shorten, but you still wouldn't be ahead of it - and thus not in the black hole. If you want cross the black horizon, you would need to essentially crash into the object ahead of you to do it.

That's why it's sorta like a Zeno's paradox.

Yes! This is EXACTLY like a Zeno's paradox. I didn't know the name of it, or I woulda said that at the very beginning. It's also wrong for the same reason that Achilles will obviously surpass the tortoise.

The Schwarzschild radius is the radius at which light cannot escape the gravitational pull of the black hole. As you get closer and closer to that radius, from the outside, it takes longer and longer for any light that started there to get to the outside. It's not that an infalling object never actually passes the horizon, but that you will never see the light from it as it did so, and the light you see from just before it fell in takes an extraordinarily huge amount of time to reach you. Something like that.

[Lagslayer]

But if you never observe it getting into the black hole, then how can you enter the black hole yourself? You'd need to do it after the object ahead of you does it, and it essentially never does as long as you're still outside. The distance between you would shorten, but you still wouldn't be ahead of it - and thus not in the black hole. If you want cross the black horizon, you would need to essentially crash into the object ahead of you to do it.

That's why it's sorta like a Zeno's paradox.

Yes! This is EXACTLY like a Zeno's paradox. I didn't know the name of it, or I woulda said that at the very beginning. It's also wrong for the same reason that Achilles will obviously surpass the tortoise.

The Schwarzschild radius is the radius at which light cannot escape the gravitational pull of the black hole. As you get closer and closer to that radius, from the outside, it takes longer and longer for any light that started there to get to the outside. It's not that an infalling object never actually passes the horizon, but that you will never see the light from it as it did so, and the light you see from just before it fell in takes an extraordinarily huge amount of time to reach you. Something like that.

+1

[Gigaz]

It's actually not quite like this.
For the far observer, an object really never reaches the event horizon, that's not just an effect which arises from the observation of the object with light.
However, if we say it never reaches the horizon that's like saying a rolling ball will never really stop rolling due to friction, its velocity just approaches zero till the end of time. In reality, such a ball will rather soon stop rolling. (when its kinetic energy reaches the termal kinetic energy of the surrounding molecules)

[Il Palazzo]

Eh. The elephant is all wrinkly! No, it's all stout like a tree! No, it's soft and prehensile!

I wish only people who actually understand GR spoke from now on. Not that I'm not guilty as any other here, though.

[Lagslayer]

Eh. The elephant is all wrinkly! No, it's all stout like a tree! No, it's soft and prehensile!

I wish only people who actually understand GR spoke from now on. Not that I'm not guilty as any other here, though.

I think part of this discussion involves challenging the common interpretation of GR.

[Putnam]

You wouldn't be spaghettified before the event horizon with a sufficiently large blackhole. The radius increases linearly with mass, remember, so the density of the black hole (including all volume encompassed by the event horizon) decreases quadratically¹ with mass. Sagittarius A*, the black hole at the center of the Milky Way, would most likely not spaghettify you. Of course, you'll still die to the light that orbits it at the event horizon's radius*1.5, which is probably a simply ludicrous amount of light.

¹ gives kg/m³

[Lagslayer]

...so, discussion on "what would happen when you fall into a black hole?" Well, assuming you weren't spaghetti'd (which you would be), then I think this page, written by people who actually know what they're talking about, should be useful.

That didn't really address any of the issues brought up. It goes on about the conclusions, but has little to nothing about how they were reached.

[Sergarr]

...so, discussion on "what would happen when you fall into a black hole?" Well, assuming you weren't spaghetti'd (which you would be), then I think this page, written by people who actually know what they're talking about, should be useful.

That didn't really address any of the issues brought up. It goes on about the conclusions, but has little to nothing about how they were reached.

You should explore that site more. The links above lead to different sections of that site, where you'll find your explanations and also this picture:

Spoiler: behold the double waterfall (click to show/hide)

[Lagslayer]

-snip-

Again, it's all based on the same assumptions, with the different models just being arguments about what's on the other side. You can't use something as evidence of itself.

[Sergarr]

-snip-

Again, it's all based on the same assumptions, with the different models just being arguments about what's on the other side. You can't use something as evidence of itself.

They... don't use something as an evidence of itself? They use various models based on general relativity... they don't just assume things.

Or do you want the evidence for general relativity itself?