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So how DOES a black hole form?

HansMustermann said:
Well, mass obviously has to move, that part I can grok. But it's exactly the details that give me a headache. And exactly the part about gravitational waves.

I mean, let's take two black holes, happily spinning around the centre of mass, more or less. Hell let's throw one more at a distance around it too. And everyone goes happily around their eliptical orbits.

If it's normal stars, I can understand it. But if everyone is holding their cards close to the chest... err... their mass behind an event horizon... umm... HOW? I can't even begin to ask a more specific question than just: HOW?
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Perhaps the problem is that you're still trying to think of gravity like a force. But it isn't.

You say you have no problem with a black hole just sitting there. But what does that actually mean? All it means is that it's following a geodesic through an otherwise flat spacetime. It doesn't "move" because it has no reason to do anything other than follow a geodesic (of course, if you shift reference frames, that stationary black hole is now moving, but it's still following a geodesic).

But what happens if spacetime isn't otherwise flat? Well, it's still going to follow a geodesic, because it's still got no reason to do anything else. It's just that now, a geodesic doesn't look like a straight line to you anymore. So it will orbit another black hole. But all that orbit consists of is following a geodesic. A black hole doesn't have to do anything to follow a geodesic. Following a geodesic is actually doing the least possible. It would have to not follow a geodesic to avoid orbiting, and that is what would require an explanation.
 
HansMustermann said:
Well, I can dig that. In fact, if the black hole sits still, it's not confusing me. It's just when the singularity moves that I start to need another beer just so I don't get a headache.

What troubles me is that the "cage" is not actually a separate entity moving with the "charge", but an effect of the "charge".

Let me use an analogy I've used before, namely the usual deformed sheet analogy for gravity. I have such a sheet, I put two balls on it, they deform the sheet, the start rolling towards each other. Yay, gravity.

I move one of the balls around, the other follows it around.

BUT the information can't move around faster than the speed of sound in the sheet.

Now let's make a black hole. I push on the sheet with the tip of a knitting needle (the singularity) and essentialy push it infinitely down in one place. The sheet is stretched so hard that at some point there's no way even theoretically to get out of that well or send any signal out of that well. The radius where that happens is the Schwarzschild radius.

And it's not a separate cage, but the result of that tip pushing down.

As long as that sits still, sure, there's no problem. The well formed already, it's there.

But now let's say I wiggle the tip of that knitting needle around. The singularity moves. How does the "cage" follow it around?

Well, that information would also have to get out of the well, which we just said it can't. That's a gravity wave telling other objects that the singularity just moved. But that wave can't actually get outside. The only way it can go is to the singularity, but it's already there, so essentially it goes nowhere.

It seems to me like that information that the "charge" just moved, can't reach the "cage". Sure, the "cage" will still say that, yep, there's that much charge there. But, as you said, it can't tell you that the "charge" just moved inside. And in fact, in the way I picture it, even it can't tell that the "charge" just moved, so it can follow it around.
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Technically the information your asking of, where the well is in relation to objects outside the event horizon, is already outside the event horizon. Information about where the singularity is doesn't have to escape the well for the well to accommodate where the singularity is in relation to the well. Information about where the well is in relation to other external objects is already external to the event horizon by virtue of it's dependence on those objects and part of the well itself being external to the, well, event horizon.

Again the problem comes in thinking of gravity as something that emanates form the gravitating body or singularity. As opposed to just the geometry of space-time which includes the event horizon. This of course makes problems when trying to consider a graviton theory similar to QED or QCD


https://en.wikipedia.org/wiki/Quantum_electrodynamics

https://en.wikipedia.org/wiki/Quantum_chromodynamics

How are the gravitons emitted and absorbed, by what and how do they interact with each other, space-time in general or other virtual particles. Just as above they would have to be an aspect of the well itself and not the singularity or gravitating body.
 
Well, I suppose it does come more instinctive to think of gravity as a force, but I'm at least trying to think of it as stretched space. But, the problem that confuses me is when the geometry changes, because a bunch of stuff deforming it moves around. Because, the way I understood it, this change deformation also has to propagate, and it does so at the speed of light.

And when I throw in a couple of coordinate singularities in there, then I have problem even imagining how this information propagates from one to another and viceversa.
 
HansMustermann said:
Well, I suppose it does come more instinctive to think of gravity as a force, but I'm at least trying to think of it as stretched space. But, the problem that confuses me is when the geometry changes, because a bunch of stuff deforming it moves around. Because, the way I understood it, this change deformation also has to propagate, and it does so at the speed of light.
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Sure. But it doesn't have to propagate from the singularity. The field interacts with itself. The change can propagate from outside the event horizon.
 
Well, that's what I don't understand. The centre of mass of the black hole moved around. How does that information get out of the event horizon in the first place? Or if it doesn't need to propagate outside, which is what you seem to be trying to tell me, then, well... HOW?

I feel like I'm missing some crucial piece of information there.
 
Darat said:
To paraphrase Hawkins we are seeing the breakdown of English in describing reality when discussing black holes, English is simply not up to the task!
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This, totally. I've mostly given up on reading about cosmology because I distrust the analogies and could never say with authority some of the things declared on this thread. And I don't get it, because I'm a fairly educated person; I have a decent understanding of Newtonian physics. But anything after the turn of the century (19th to 20th), forget it. I've run into this hard limit that I first reached in high school, have not been able to move past it and don't know how to transcend it.

If words were sufficient, anyone could read about it and understand it. Not my experience.
 
Ziggurat said:
Did it? In what reference frame?

In its own reference frame, it didn't.
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And now you see why I need more beer just to not go cross eyed there. I swear, physics is driving me to alcoholism ;)

Well, more seriously, if you have three black holes merrily orbiting around, no matter which of them you take as reference, the other two are moving. And in fact accelerating. I knew there was a reason I was sticking to three bodies.
 
Minoosh said:
This, totally. I've mostly given up on reading about cosmology because I distrust the analogies and could never say with authority some of the things declared on this thread. And I don't get it, because I'm a fairly educated person; I have a decent understanding of Newtonian physics. But anything after the turn of the century (19th to 20th), forget it. I've run into this hard limit that I first reached in high school, have not been able to move past it and don't know how to transcend it.

If words were sufficient, anyone could read about it and understand it. Not my experience.
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Well, I used to have no problem with the words or with the maths. It's just at the end of high school I decided to not go to a physics college. And it was decades ago, so I forgot even a chunk of what I knew too.

THAT said, I guess not everyone thinks in the same way, or has the same interests. BUT IMHO it also depends on who's explaining it to you. Teachers range from very good at explaining stuff, to outright awful. E.g., I hated history in school, because it was just a dry exercise in rote memorization of dates and names, but after school I discovered that man, that thing is super-interesting if I read it on my own terms. Same goes for other subjects, IMHO.
 
HansMustermann said:
And now you see why I need more beer just to not go cross eyed there. I swear, physics is driving me to alcoholism ;)

Well, more seriously, if you have three black holes merrily orbiting around, no matter which of them you take as reference, the other two are moving. And in fact accelerating. I knew there was a reason I was sticking to three bodies.
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But they aren't accelerating locally. They are in free fall, which is the closest you can get to being motionless in GR.
 
I get that. But #1 is our reference, #2 and #3 are in free fall in regards to it, but also to each other. And that's where the coordinate singularities confuzzle me.
 
HansMustermann said:
I get that. But #1 is our reference, #2 and #3 are in free fall in regards to it
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No, they are not. #1 and #2 are accelerating in regards to our frame. They are in free fall in regards to their own frame.

Frames can only be inertial locally in general relativity.
 
Well, now you've confused me. I mean, they're accelerating was my initial guess in #109, but apparently that was wrong...
 
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HansMustermann said:
And I really like the guy. He's good at explaining stuff. I'll look for more of his lectures.
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Yeah I'm a big fan of his. He's got several these lecture series that are very well done and interesting.

He also has a few books which are excellent.

I'm going to recommend one my favourite lectures of his, I think you will really enjoy it:

"ER = EPR" or "What's Behind the Horizons of Black Holes?"
https://www.youtube.com/watch?v=OBPpRqxY8Uw

Given that title it's still somewhat on topic for this thread. :boxedin:
 
HansMustermann said:
Well, now you've confused me. I mean, they're accelerating was my initial guess in #109, but apparently that was wrong...
Click to expand...

They are accelerating, in your frame. They are not accelerating, in their own frame. But their frame, not yours, is the important one for this, because their frame is inertial around them, and yours isn't.
 
Well, let me put my problem differently. We have a bunch of bodies deforming the space and moving through that deformed space. Like the black holes going around the big one at the centre of the galaxy.

Now I already understand that each one of them is just following a geodesic, falling freely, and all that. It's obvious. It's literally the least it can do.

I get that. (Or at least I think I do. It could be Dunning-Kruger speaking.)

But as the configuration of the system changes, as these things move around each other, the geometry of that space changes. Those geodesics wave and swirl around over time. Am I wrong so far?

And they do so because of mass.

And that information propagates at the speed of light. 'Cause, you know, that's the speed limit. It's the law.

And that confuses me when I throw in a couple of coordinate singularities into the mix.

And here's WHY it confuses me: let's step back from black holes, and look at the Earth and the Moon. Now you can approximate them as two points, but that's just to simplify the maths. Actually every piece of mass composing the Earth is gravitationally interacting with each piece of mass composing the moon. It being equivalent to calculating just for the centres of the spheres is actually the result of integrating all that. We're just skipping the actual integral because Messrs Newton and Birkhoff did it for us in their respective theorems, but basically that's the part that is implicitly there: integrating over the whole volume of Earth and respectively the Moon.

But actually it IS a collection of bits interacting with each other, or we wouldn't have tidal forces. Meaning we wouldn't have the tides on Earth, or a Roche limit, or for that matter the rings of Saturn, or tidal heating on Titan, or we wouldn't have the Moon or Mercury be tidally locked. All those happen when bits on one side experience space curvature differently enough than bits on the other side.

Basically, sure, the Earth or the Moon follow the geodesic, but that's really just integrating where the geodesic points for each point inside them.

But throw in an event horizon or two between them, and I'm totally confused about which bits interact with which bits there.
 
Mass creates curvature. Mass responds to curvature. When mass responds to curvature, it doesn't matter where the curvature came from. All that matters is that the curvature is there.

Furthermore, you actually cannot do what you suggest in General Relativity. Yes, in Newtonian mechanics, you can figure out the total gravitational force from the earth by adding up the little bit of force from each little bit of the earth. And you can do so because the theory is linear: it's a force, and the forces just add.

But General Relativity is not a linear theory. It's approximately linear at low masses, but it's highly non-linear by the time you get to black holes, which is what you're talking about. So just adding up the effects from each bit of mass doesn't work. Calculating the field is more complicated. If you like, you can think of it like the field created by each bit of mass interacting with the fields of all the other masses to create additional fields. The more mass you have, the stronger the field, the bigger these interactions and nonlinearities become. And when you've got two black holes, those fields are really strong, and the nonlinearities are really big. At that point, it's OK to think of it as the fields orbiting each other. And the fields don't need to escape the event horizon, they're already outside.
 
Well, Birkhoff managed to integrate it just fine, from what I understand. Granted, I expect it to be a lot more complicated than in Newton's case, but obviously it's not impossible.

Edit: And, well, I could think of it in a number of simplified ways, but I usually like to understand why that simplification is ok. Mass creates curvature, and mass responds to curvature. But curvature doesn't create curvature (well, it propagates, but that's another thing), nor does it respond to curvature. I don't see how the simplification of just the fields orbiting each other is justifiable in any way. Which probably just means I'm missing some info, so please do explain if you have the time. It's very much appreciated.
 
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