So how DOES a black hole form?

[Reality Check]

But throw in an event horizon or two between them, and I'm totally confused about which bits interact with which bits there.

The answer is exactly the same "bits" that interacted before the event horizon was there. Gravitation is an effect of spacetime being curved. An event horizon is merely a region in curved spacetime that has significant non-gravitational physical effects.

 

[Reality Check]

Well, Birkhoff managed to integrate it just fine, from what I understand.

Birkhoff did not integrate over multiple objects. His theorem is for 1 object.
Birkhoff's theorem

In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution (i.e. the spacetime outside of a spherical, nonrotating, gravitating body) must be given by the Schwarzschild metric.

 

[HansMustermann]

The answer is exactly the same "bits" that interacted before the event horizon was there. Gravitation is an effect of spacetime being curved. An event horizon is merely a region in curved spacetime that has significant non-gravitational physical effects.

Well, MY problem is that now from either side you look at it, for black holes revolving around each other, some of those bits are behind an event horizon. So when the whole thing moves around, well, one set of bits of matter can't observe that the other set of bits of matter moved.

That's what confuzzles me.

Birkhoff did not integrate over multiple objects. His theorem is for 1 object.
Birkhoff's theorem

Well, yes, but that's essentially why you can treat one of the objects as a point, when dealing with its influence on the individual bits of the other object. E.g., to calculate the tidal effects on something orbiting a black hole.

Besides, if it were fundamentally impossible to now integrate that on the other object as well, you just told me that there's zero justification in approximating such a system as two points. I'm not an expert on GR, mind you, but I like to think that physics doesn't just pull such approximations out of the rear end.

 

[Ziggurat]

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.

Of course curvature responds to curvature. Gravitational waves will bend just like light does in a gravitational field.

ETA: and that's also why gravitational waves can't escape the event horizon.

 

[HansMustermann]

Yes, well, my bad choice of words. I almost put a disclaimer on that one too, and it looks like I should have.

My point is that generally doesn't in the same way as the matter that generates that curvature. That is, unless that mass also has zero rest mass. The gravity waves from, say, the moon, will not go round and round the Earth, because the space is not THAT curved, but the moon does. I don't even have to do the maths, because I can look at what the light from the moon does. It totally doesn't go in the same orbit as the moon.

My point is that I can't just ignore the matter and pretend it's just the deformation from the Earth and the Moon interacting with one another. Because just looking at what the gravity waves do in that deformation will yield a fundamentallly different result than what something with non-zero rest mass and a different speed to boot does there.

 

[Ziggurat]

Yes, well, my bad choice of words. I almost put a disclaimer on that one too, and it looks like I should have.

My point is that generally doesn't in the same way as the matter that generates that curvature. That is, unless that mass also has zero rest mass. The gravity waves from, say, the moon, will not go round and round the Earth, because the space is not THAT curved, but the moon does. I don't even have to do the maths, because I can look at what the light from the moon does. It totally doesn't go in the same orbit as the moon.

Sure, gravitational waves and light from the moon don't orbit earth. Neither does asteroid 2017 BH30, even though it got closer to earth than the moon.

My point is that I can't just ignore the matter and pretend it's just the deformation from the Earth and the Moon interacting with one another. Because just looking at what the gravity waves do in that deformation will yield a fundamentallly different result than what something with non-zero rest mass and a different speed to boot does there.

The curvature of a far field gravitational wave is different than the curvature surrounding a mass. Why would you expect the interaction of different curvatures to be the same?

I specified far field because the interaction we're discussing actually produces gravitational waves.

 

[Reality Check]

Well, MY problem is that.....

That is YOUR problem because gravity does not stop at an event horizon as you seem to think.
Thus "some of those bits are behind an event horizon" and when the whole thing moves around, every set of bits of matter observes that every other set of bits of matter moved.

Birkhoff's theorem means that we can treat any spherical, not rotating, not charged body as a point mass. If we have many spherical, not rotating, not charged bodies then we treat them all as point masses. That leads to the problem in GR that there are no exact solutions for any systems with 2 or more bodies. This is the equivalent of the 3-body problem for Newtonian gravitation and has similar workarounds. There are approximate solutions for one body much lighter than the other. We can use numerical simulations.

Thus there is justification in approximating your system as two point masses. However for real black holes there is almost zero justification because they spin. We could approximate as a point mass and know that it does not change the dynamics of an orbiting body very much far from the black hole. We also know that as soon as that body gets close to the event horizon all bets are off!

 

[HansMustermann]

Well, I never said that gravity stops at the event horizon. Gravity waves, however, which is how you observe that those bits moved, do. Well, in one direction. Gravity waves can't even reach the event horizon from the inside, which is where a black hole's bits are. There's no way for them to go than towards the singularity, without exceeding the speed of light.

And yes, it is MY problem, because I'm the one that's still confused by how that works.

 

[Ziggurat]

That is YOUR problem

That's not really fair to Hans. Yes, it's his problem, but he's trying to solve it. There's nothing wrong with not understanding something as complicated as General Relativity. Nor is there anything wrong with trying to understand it, even if it's ultimately beyond him. I've never once seen any suggestion from Hans that he thinks GR is wrong, that it's woo or a conspiracy, only that he can't fill in these gaps in his understanding of it. And at the end of the day, without learning all the math involved (no easy task, and probably beyond the scope of this forum), maybe he never will. But that's OK.

 

[HansMustermann]

Well, I _AM_ starting to suspect that I'm reaching some limit of my understanding, at least for now.

To make it clear in case it wasn't clear, I actually believe that GR is right, at least to the extent we were able to confirm it. If it weren't, well, GPS wouldn't work for a start. Plus, smarter people than me have peer-reviewed it. Same for QM, incidentally. The computer I'm on wouldn't work if QM didn't work. So, no sane reason for me to disbelieve either.

I'm even sorta able to follow the simplest cases. I think. Or it could be Dunning-Kruger speaking. But when it starts happening around extreme cases like a black hole that my, shall we say, intuition fails me miserably.

Still, on the bright side, I have learned a couple of new things anyway, and even more from watching a couple of Susskind's lectures which were also suggested here. I'lll work my way through more, as time allows. So, many thanks for everyone's time and patience.

I suspect the only sane way to get much further would be to just go back to college. Or find some professor that's willing to tutor me for money. Hmm, might not even be that expensive if I find someone from India or China or such to teach me over the internet... I'll have to think about it.


To get back one more time to my comprehension problem, though, it actually stems from the last phrase in your message #126. "[/i]I specified far field because the interaction we're discussing actually produces gravitational waves.[/i]" That part I get. The change in the field's geometry propagates as a wave at the speed of light.

But I just can't seem to "follow" that wave when there are event horizons around, basically.

What exactly do you mean by "the interaction" above, though? I mean, when mass is involved, I can get that. But do you mean that just the interaction of two fields generates waves as well, as opposed to being the superposition of waves from the two? THAT might be the piece I was missing, IF it works that way.

 

[Ziggurat]

What exactly do you mean by "the interaction" above, though? I mean, when mass is involved, I can get that. But do you mean that just the interaction of two fields generates waves as well, as opposed to being the superposition of waves from the two? THAT might be the piece I was missing, IF it works that way.

GR is a nonlinear field theory. In any nonlinear field theory, the field interacts with itself. If it didn't interact with itself, then it would be linear. Since it's not linear, you don't get simple superpositions of fields. The total is not just the sum of the parts.

Let's take the specific case of two black holes orbiting each other. They will emit gravitational waves as they orbit. Where are the waves coming from? Not from the singularity. Gravitational waves can't escape the event horizon. The waves are coming from the interaction of the curvature of both black holes, as they warp around each other. The waves come from the whole structure.

 

[HansMustermann]

Ooooh... NOW I get it. Thanks. THAT was the piece I wasn't quite getting.

 

[Pixel42]

I suspect the only sane way to get much further would be to just go back to college. Or find some professor that's willing to tutor me for money. Hmm, might not even be that expensive if I find someone from India or China or such to teach me over the internet... I'll have to think about it.

Or you could do a free online course. The first one on this list looks suitable:

http://academicearth.org/physics/

 

[Reality Check]

Gravity waves,...

Gravitational waves (gravity waves are not gravitational waves) are how we observe masses undergoing enormous acceleration in the last couple of seconds of their merger. That is the LIGO and now VIRGO observations. These waves stop once the black holes have merged.

We do not (and as far as I know cannot) observe gravitational waves from "bits" inside of event horizons.

 

[HansMustermann]

No, that part was clear. (Well, except for my terminology mix-up. It's not always easy to ask these things in a foreign language, so thanks for the help there.) It was in fact why I was asking.

The only thing that wasn't really sinking in was the last thing that Ziggurat cleared up in #131. Actually, now with that bit of information, a couple more things are a lot clearer too, not just the issue of black holes orbitting each other.

I guess that's the problem with not really understanding something. Sometimes I don't even know WHAT to ask. So basically that's why this went on for 4 pages.