So how DOES a black hole form?

[The Man]

I will concede as rather obvious that, yes, there is no actual event horizon inside the shell, since it's all flat space in there. We can calculate where that horizon would be, but yep, it ain't there yet.

BUT that brings me back to the original question. From the frame of a distant observer, that would kinda be what a "black hole" really looks like, innit? Mind you, the shell would probably be within planck lengths of the Schwarzschild radius, if it's got billions of years (again, in the frame of an external and distant observer) to fall in, and that shell's been red-shifted into being blacker than black, so essentially it would look indistinguishable from an actual black hole by any practical measurement. You couldn't really tell if the Schwarzschild metric begins at the actual event horizon or picometres from it by any measurement from light years away.

But my question is really a theoretical one, really. And to make it clearer about which frame and whatnot, it's really this that got me thinking: let's say we have a star orbiting a black hole. Like, say S2, a.k.a. S0-2, one of the stars orbiting real close to Sagittarius A, the supermassive black hole at the centre of our galaxy. Well, about 17 light hours way, so time and space will get WEIRD there, but that's not relevant.

And my question was really just this: from the frame of S0-2, is it observing that it orbits around an actual black hole, with the mass inside its Schwarzschild radius, or around an empty shell just outside Sagittarius A's Schwarzschild radius? I'm thinking that from the perspective of S2, it's orbitting around that shell, innit?

Of course, from the perspective of something that already fell into Sagittarius A, it's inside the event horizon of a proper black hole and it probably hit the singularity at the centre billions of years ago. But that's not what I'm asking.

Not according to the hoop conjecture, the mass is already inside the hoop (the Schwarzschild radius) for the black hole and event horizon to form.

 

[HansMustermann]

Hmm, interesting. I'll have to study that some more. Can you please elaborate on how does the matter get to be already inside the event horizon (from the pov of someone outside and at a distance)? I find that proposition really fascinating.

ETA: MY understanding of the hoop conjecture (which is probably wrong, but just so someone can correct me if I am) is that the hoop radius is not the same as the Schwarzschild radius. In fact, it's 2*Pi times bigger than the Schwarzschild radius. So in fact the hoop conjecture would be no constraint for what I'm proposing. I mean, for example for Sagittarius A, the hoop radius woulld be 2*Pi*6.7 billion km, or basically extend some 35 billion km outside the event horizon of Sagittarius A, whereas most of the shell I'm talking about would be within something like picometres outside the event horizon. So basically it's nowhere NEAR being outside of the hoop too.

 

[Ziggurat]

I will concede as rather obvious that, yes, there is no actual event horizon inside the shell, since it's all flat space in there. We can calculate where that horizon would be, but yep, it ain't there yet.

No, it IS there. It's just that it means less than you might suppose.

BUT that brings me back to the original question. From the frame of a distant observer, that would kinda be what a "black hole" really looks like, innit?

Sure. But that just brings us back to the distinction between what you see and what you observe.

Let's take, for example, the famous twin paradox in special relativity. You are earth-bound, your twin zooms off and comes back. As he moves away from you, he sees you red-shifted and your clock running slower. As he moves back toward you, he sees you blue-shifted and your clock running faster. But both times, he observes that, relative to him, your clock runs slower (the blue shift is just from Doppler effect). But you end up older. So how do you end up older if he always observes your clock running slower?

If you want to solve this by looking at what he observes, then you have to include what happens when he turns around. You get that the line of simultaneity for the traveling twin is tilted compared to the earthbound twin, right? When he's moving away from you, the tilt is such that when he's just before the halfway turnaround point, he observes that much less than half your time has passed. And when he's moving towards you, the tilt is such that when he's at the halfway point, he observes that much more than half your time has passed. Accelerating in his frame changes the tilt of his line of simultaneity, and so makes your time appear to him to rapidly advance. But that's an artifact of the non-inertiality of his frame. Nothing strange is actually happening to your time.

Now, what happens to this line of simultaneity if your twin approaches you and then reverses to go away from you? Well, it will tilt such that, if you're far enough away, he will observe time flow backwards for you. He never sees that, but that's what he observes. Again, it's an artifact of non-inertiality. Same thing with the acceleration-produced event horizon: it's an artifact of non-inertiality.

In the case of the twin paradox, none of this is terribly important, and generally doesn't even get touched upon. Why not? Because we don't need to deal with non-inertial frames in special relativity. We can analyze everything from an inertial frame (even if the path we're analyzing accelerates), so all the complications of non-inertial frames are avoidable.

But they aren't avoidable in general relativity. You must deal with non-inertial frames. It's not possible to construct frames with are globally inertial. So stuff gets weird.

But there are still analogues. The artificial event horizon in SR? Time apparently stopping? That's because you keep accelerating. Stop accelerating, cross that artificial event horizon, and everything starts up again. Well, the same applies here: stop continually accelerating (ie, fall into the black hole), cross the event horizon, and you can see that time didn't stop. It was just an artifact of your non-inertiality.

And my question was really just this: from the frame of S0-2, is it observing that it orbits around an actual black hole, with the mass inside its Schwarzschild radius, or around an empty shell just outside Sagittarius A's Schwarzschild radius? I'm thinking that from the perspective of S2, it's orbitting around that shell, innit?

If the shell were actually stationary, then it would look different, since it will stop redshifting further. But it's impossible to tell for certain, from the outside, that the shell won't stop collapsing at some point. Just like we can't tell for sure that the stars we observe in the sky haven't already exploded, because it takes time for the signal to reach us. You could also say that it takes asymptotically longer for the light to escape, so you don't know what's happening "now", but absent a mechanism to stop the collapse you could still say it has already finished.

 

[W.D.Clinger]

And my question was really just this: from the frame of S0-2, is it observing that it orbits around an actual black hole, with the mass inside its Schwarzschild radius, or around an empty shell just outside Sagittarius A's Schwarzschild radius? I'm thinking that from the perspective of S2, it's orbitting around that shell, innit?

Orbiting around a spherical shell just barely outside a radius r is just barely distinguishable (if at all) from orbiting around a point mass at its center. That doesn't depend on whether the object being orbited is a black hole. With a black hole, however, there may be other indications that something funny is going on.

Basically. "black holes don't exist" or "back holes never finish forming" strictly from the perspective of a distant observer. No more, no less. And the answers so far (filtered through my very limited knowledge) lead me to think that that's actually correct.

A distant observer won't actually see anything going on at the event horizon or inside. On the other hand, a distant observer who understands general relativity will be able to infer certain things, so it really comes down to whether you want the word "observe" to include inferences based on general relativity combined with what can be seen and measured.

In particular, a distant observer can be aware that the Schwarzschild coordinate system is limited to a proper subset of spacetime, and can use other coordinate systems to calculate, taking advantage of the known continuous transformations between the disparate coordinate systems where they overlap.

 

[HansMustermann]

@Ziggurat
In a different time frame, sure it has already finished. All I'm saying is that from the reference frame of S0-2, all the mass of Sagittarius A is a shell outside, innit? I wouldn't call it a stationary shell, but one that moves slower and slower the closer it gets to the coordinate singularity. Pretty much BECAUSE it's a coordinate singularity.

That said, I will agree with you again that, yes, if you're actually falling into the black hole, you're totally gonna cross the event horizon in your own reference frame. You're totally not gonna get stuck outside in that frame. In fact, not only you're not gonna be slowing down, but you'll probably be going close to the speed of light by the time you cross.

 

[HansMustermann]

A distant observer won't actually see anything going on at the event horizon or inside. On the other hand, a distant observer who understands general relativity will be able to infer certain things, so it really comes down to whether you want the word "observe" to include inferences based on general relativity combined with what can be seen and measured.

Well, "see" is more theoretically speaking. As in, I'm within a light cone centered in a piece of matter there, rather than actually detecting a photon actually emitted by that piece of matter.

And to be honest, my interest in this all is mosty about gravity anyway, rather than photons. And I think we're getting plenty of gravity there to observe that something's funny over there. But it just happens that gravity is still constrained by a light cone AFAIK, so it's kinda the same discussion.

ETA: but yes, I will concede again that some reasonably educated standing on a planet of S0-2, could infer that from the perspective of a piece of matter falling into Sagittarius A, it'll be over rather quickly, rather than taking infinity.

 

[The Man]

Hmm, interesting. I'll have to study that some more. Can you please elaborate on how does the matter get to be already inside the event horizon (from the pov of someone outside and at a distance)? I find that proposition really fascinating.

Until it is a black hole there is no event horizon. The matter is already inside the Schwarzschild radius hoop which is where the event horizon forms.

ETA: MY understanding of the hoop conjecture (which is probably wrong, but just so someone can correct me if I am) is that the hoop radius is not the same as the Schwarzschild radius. In fact, it's 2*Pi times bigger than the Schwarzschild radius. So in fact the hoop conjecture would be no constraint for what I'm proposing. I mean, for example for Sagittarius A, the hoop radius woulld be 2*Pi*6.7 billion km, or basically extend some 35 billion km outside the event horizon of Sagittarius A, whereas most of the shell I'm talking about would be within something like picometres outside the event horizon. So basically it's nowhere NEAR being outside of the hoop too.

It is the circumference of the hoop that is given by "2*Pi times" Schwarzschild radius. Thus the radius of the hoop is the Schwarzschild radius.

 

[Delvo]

Not according to the hoop conjecture, the mass is already inside the hoop (the Schwarzschild radius) for the black hole and event horizon to form.

Can you please elaborate on how does the matter get to be already inside the event horizon (from the pov of someone outside and at a distance)? I find that proposition really fascinating.

Most of it was already inside the spherical region in question before that region became the inside of a black hole. For a neutron star with such a mass that its Schwarzschild radius is 5 miles (several times the sun's mass), and an actual radius of 5 miles and 3 feet, the inner 10-mile-wide region of the star is already inside the Schwarzschild sphere, so your questions only apply to the outermost 3-foot-thick crust. Regardless of what happens to that crust, those inner several suns' worth of mass in the 10-mile-wide core below it, already inside the Schwarzschild sphere, couldn't possibly fail to end up inside any black hole that forms from the star.

ETA: MY understanding of the hoop conjecture (which is probably wrong, but just so someone can correct me if I am) is that the hoop radius is not the same as the Schwarzschild radius. In fact, it's 2*Pi times bigger than the Schwarzschild radius.

That's the circumference, not the radius. The "hoop" is a description of the same basic concept as the original Schwarzschild radius definition. The only difference is consideration of non-spherical shapes: what happens to an object which has lengths/widths above the Schwarzschild diameter in some directions but below it in others? The hoop conjecture is that you don't get a black hole until it's small enough in every direction, not just some directions. But it really doesn't matter because every real object for which conversion to a black hole is even a question is spherical anyway. And the process of the Schwarzschild sphere growing until it envelops the required mass is not dependent on it.

 

[HansMustermann]

Ah. Just shows I had gotten the hoop wrong after all. Thanks, guys.

 

[HansMustermann]

THAT said, I'm still not in the clear as to how it applies to my question. Just shows I have much to learn, I guess.

I will happily grant that any matter that was inside the Schwarzschild radius before the black hole formed, will probably stay inside after the collapse is complete. A neutron star that started imploding, well, it already can't support its own weight, much less eject from the core. And from its perspective, the black hole will finish imploding all right.

Still doesn't answer my question about the perspective of a distant observer, though.

 

[HansMustermann]

Well, probably I should clear my thoughts, since I've obviously been just confusing so far. And I should probably throw in some details about exactly what my interest is in the gravity of the situation. Because maybe there's a simpler answer in that direction.

It actually ties in with one of my previous threads from long ago, about the gravity of a moving black hole. Basically, let's return to S0-2. It revolves around Sagittarius A, which is a supermassive black hole. BUT Sagittarius A in turn doesn't just stay still. It moves around or towards other things, like for example the Great Attractor at the center of the Laniakea Supercluster.

And here's what confuzzles me: if, from the perspective of S0-2, the mass of Sagittarius A is behind an event horizon, it can't possibly receive any information about it moving around. Because it's in that middle-upper triangle in a Penrose diagram for a Schwarzschild metric. Gravity is just as constrained by a light-cone as anything else, and basically any information from inside the event horizon, including gravity shifts, can't end up in any other place than the singularity. Best it can do at light speed is go at 45 degrees and eventually hit the singularity.

If, however, S0-2 "sees" all the mass of Sagittarius A as a shell outside the Schwarzschild radius -- and I mean "sees" as there IS a light cone from any of it to S0-2, regardless of whether any actual light from it is detectable -- then I can jolly well understand why and how S0-2 follows the movement of Sagittarius A. Because there's really no barrier to its receiving that information.

That's also why I'm not very interested for the scope of this particular question, in what other metrics or coordinates would apply to the matter that did fall into Sagittarius A. Nor in what an intelligent observer from around S0-2 would logically and mathematically infer about the formation of Sagittarius A. Because S0-2 isn't very intelligent or prone to doing any maths or smart inferences. It's just a star following a path set by space-time distortion.

Mind you, I know that something being confusing to me doesn't mean it's wrong. But, well, maybe someone can clear up that confusion for me, so I don't have to end up wondering about it at 2:30 AM

Edit: I think I'm starting to figure it out. They're just moving together in the gravity well of the great attractor, innit?

 

[Ziggurat]

And here's what confuzzles me: if, from the perspective of S0-2, the mass of Sagittarius A is behind an event horizon, it can't possibly receive any information about it moving around. Because it's in that middle-upper triangle in a Penrose diagram for a Schwarzschild metric. Gravity is just as constrained by a light-cone as anything else, and basically any information from inside the event horizon, including gravity shifts, can't end up in any other place than the singularity. Best it can do at light speed is go at 45 degrees and eventually hit the singularity.

If, however, S0-2 "sees" all the mass of Sagittarius A as a shell outside the Schwarzschild radius -- and I mean "sees" as there IS a light cone from any of it to S0-2, regardless of whether any actual light from it is detectable -- then I can jolly well understand why and how S0-2 follows the movement of Sagittarius A. Because there's really no barrier to its receiving that information.

That's one way of looking at it. But it's not the only way. Here's another.

Have you ever heard of Gauss's law? Basically, if you take any closed surface, the electric field flux through the surface is proportional to the charge enclosed by that surface.

Now, Gauss's law doesn't tell you how the charge is distributed inside the volume enclosed by the surface, but that's not important for the moment. The important point is that the field at the surface contains information about the charge inside. And that's true no matter how big a surface you draw.

In Newtonian gravity, Gauss's law works the same for gravitational field and mass. Of course, Newtonian gravity is wrong, but there's still an analogue for Gauss's law in general relativity. The details are messier (of course), but the principle remains the same: spacetime curvature away from a mass gives you information about what's inside. That's true no matter what the mass is doing.

So what's the relevance here? Simply that information about the mass of a black hole doesn't need to escape the event horizon. That information is already outside. It already exists at a distance. It was before the collapse, it will remain so after the collapse. So the gravitational field won't change when collapse happens, because there's no reason for it to change. The field is already there, it's not escaping from the event horizon.

Oh, and one more note: Gauss's law for electric fields still applies to black holes. They can be charged, and the field doesn't need to "escape" the black hole to be felt.

 

[Delvo]

Gravity is just as constrained by a light-cone as anything else

The only thing stopping matter or photons from escaping a black hole is gravity. Gravity doesn't fight against gravity and doesn't need to escape from the hole. It's just a curvature of space, and the event horizon doesn't break that curvature. When physicists talk about "information" being lost in black holes, total mass is not included in that; the "information" about its mass is still observed.

You might say that, as far as the outside world is concerned, the distortion might as well be coming from the event horizon rather from inside it, but the only reason why a spherical surface would act like such a source of gravitational distortion is if it enclosed mass anyway, in which case we're back to the mass inside being the actual source.

 

[Ziggurat]

Gravitational waves cannot escape a black hole. But the field doesn't have to. Same with electric and magnetic fields: a black hole can have both, even though electomagnetic waves cannot escape.

 

[Delvo]

BTW, you are not alone in thinking that some of the behavior of event horizons and singularities doesn't seem to fit together quite right in the standard interpretation (especially in light of quantum mechanics; although both appear to be true in every test we can do so far, they don't get along in some circumstances that we haven't been able to test yet, particularly black holes and event horizons). Actual physicists have proposed alternatives to standard interpretations of relativity, to try to either deal with challenges like these or find a way to get it to cooperate with QM. These things are not mainstream, but they are taken seriously and sort of waiting in the wings to see if they might eventually pan out when more definitive evidence is available.

One example that your questions remind me of is the "gravastar", a star-derived object composed of a form of matter denser than a neutron star and behaving like a black hole in practically every externally observable way, but lacking a singularity or an event horizon or any region of space actually getting cut off from the outside by such a horizon. Even the appearance of an event horizon, in this case, is created by a combination of:
•the difficulties you raise in externally distinguishing between present real black holes and other arrangements of matter that will never quite really become black holes, and
•a QM-imposed limit on the blue-shift of incoming radiation which results in reduced temperature which makes any outgoing radiation so weak, and thus so long in wavelength, that the red-shift on top of that makes outgoing radiation seem to disappear as if there were a region it couldn't "escape" from.

Gravastars would, if the idea checks out, replicate the external observations about black holes, without the need for some of the more extreme weirdnesses of relativity or its incompatibility with QM. You could look at this as meaning that the Schwarzschild radius is not the radius at which a black hole would form but the radius that you just can't go beyond because a black hole can't form any more than you could go faster than light or divide by zero. And that goes for not only individual black holes and their interactions with other objects as observed from the outside, but also the merger of black holes; the LIGO measurements of gravity waves have recently been checked and found to fit the math for merging gravastars as well as for merging black holes. (The black hole interpretation was also not eliminated; it's just another way in which they're just about impossible to tell apart.)

But none of this has anything to do with any of the answers you've been given so far, which have been about straightforward standard black hole interpretation.

 

[HansMustermann]

That's one way of looking at it. But it's not the only way. Here's another.

Have you ever heard of Gauss's law? Basically, if you take any closed surface, the electric field flux through the surface is proportional to the charge enclosed by that surface.

Now, Gauss's law doesn't tell you how the charge is distributed inside the volume enclosed by the surface, but that's not important for the moment. The important point is that the field at the surface contains information about the charge inside. And that's true no matter how big a surface you draw.

In Newtonian gravity, Gauss's law works the same for gravitational field and mass. Of course, Newtonian gravity is wrong, but there's still an analogue for Gauss's law in general relativity. The details are messier (of course), but the principle remains the same: spacetime curvature away from a mass gives you information about what's inside. That's true no matter what the mass is doing.

So what's the relevance here? Simply that information about the mass of a black hole doesn't need to escape the event horizon. That information is already outside. It already exists at a distance. It was before the collapse, it will remain so after the collapse. So the gravitational field won't change when collapse happens, because there's no reason for it to change. The field is already there, it's not escaping from the event horizon.

Oh, and one more note: Gauss's law for electric fields still applies to black holes. They can be charged, and the field doesn't need to "escape" the black hole to be felt.

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.

 

[Ziggurat]

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, what would make the singularity move? It's not going to do so spontaneously. The only thing that's going to make the singularity move is something external, like the gravitational field of another black hole (for example).

But you don't need to know what the singularity specifically is doing. You know that there's a bunch of mass within this volume. Information doesn't have to escape for you to know that this mass is going to respond by falling in this external gravitational field. All the information necessary is contained in the field outside the event horizon. The details of what happen within the event horizon are all irrelevant, but that mass has to move. There is no possible way it can't move, because in order to resist movement, it would have to do something that would require information to escape.

You can also think about this as the spacetime curvature interacting with itself. And it has to, doesn't it? Otherwise, you can't get gravitational waves.

 

[lomiller]

I’m not sure if it applies to any distant observer but Wikipedia (I know…) has this to say:

In practice, all event horizons appear to be some distance away from any observer, and objects sent towards an event horizon never appear to cross it from the sending observer's point of view (as the horizon-crossing event's light cone never intersects the observer's world line).

 

[HansMustermann]

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?

 

[Delvo]

Because putting matter behind an event horizon doesn't "hide" it.