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So how DOES a black hole form?

HansMustermann

Penultimate Amazing
HansMustermann
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Mar 2, 2009
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Before I start, let me state that I'm not pushing any explanation of my own, because I don't even have one. Which is unsurprising, I guess, since I'm not a physicist. I genuinely get a brainfart just trying to think about how it swallows matter, and I'm hoping someone more knowledgeable can help me understand it.

Now I'm not asking about the whole thing about how many solar masses you need and all that, because that part I know already.

I'm also not asking about matter falling below the event horizon, and the Schwarzschild radius, 'cause that part is clear too.

But, here's the thing I don't get: how it gets an event horizon in the first place, and how does it get more mass.

And I'll start by stating how I understand it. Which is probably wrong, since I can't get anywhere with it. But maybe it will help someone spot and point out to me the point where I'm going into gaga land with it.

Schwarzschild calculated that limit for an eternal black hole. It has always existed and it always will. Well, that one is easy, 'cause you don't have to deal with it forming in the first place. And I know physics simplifies the model to what's relevant for the problem at hand, and I have no problem with it. (Not that it would matter to anyone else if a layman did have a problem with it, mind you.) Just it doesn't answer MY problem.

And my problem stems from the fact that we don't have anything that always existed, since the universe ain't that old. So it has to have formed at some point.

So let's say some chunk of matter swirls down the drain... err, accretion disk, and falls down into the black hole. From its point of view, of course, that happens in a finite time. From OUR frame of reference, though, time dilates increasingly the closer to the event horizon it gets, and it goes asymptotically towards the actual event horizon. So essentially it takes an infinite time for us to see it fall in. It only gets there at +infinity on the time axis.

And it doesn't help if I put it on a pinrose diagram, 'cause that line is still at infinity.

Essentially if I don't start with a pre-existing black hole, it sems to me like I can only get a FUTURE black hole, infinitely into the future. The matter never actually gets inside it, information never disappears into it, it just gets stuck at an apparent horizon, in infinitely slow motion.

So... how did it form in the first place? How can I end up with a present black hole, instead of a future one? Where am I thinking all wrong?
 
HansMustermann said:
Before I start, let me state that I'm not pushing any explanation of my own, because I don't even have one. Which is unsurprising, I guess, since I'm not a physicist. I genuinely get a brainfart just trying to think about how it swallows matter, and I'm hoping someone more knowledgeable can help me understand it.

Now I'm not asking about the whole thing about how many solar masses you need and all that, because that part I know already.
Click to expand...

When lots of masses love each other very much....
 
HansMustermann said:
Schwarzschild calculated that limit for an eternal black hole. It has always existed and it always will.
Click to expand...
Nothing so fancy:

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light.

[...]

The Schwarzschild radius of an object is proportional to the mass. Accordingly, the Sun has a Schwarzschild radius of approximately 3.0 km (1.9 mi), whereas Earth's is only about 9.0 mm (0.35 in).

[...]

Any object whose radius is smaller than its Schwarzschild radius is called a black hole. The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body (a rotating black hole operates slightly differently). Neither light nor particles can escape through this surface from the region inside, hence the name "black hole".


All you need to form a black hole is to compress a quantity of mass to a sufficiently high density. The most common compression force is gravity. The effect is self-reinforcing, too: Gravity attracts more mass, which exerts more compressive force on the body... there are repulsive forces, too. The Earth is happily able to resist further compression, since it hasn't accumulated enough mass to overcome the other forces that hold its radius outside the Schwarzschild radius for its mass.
 
Did we get to the point where we start talking about kugelblitzes yet? That might help shine light on the situation.
 
While the answers are correct, they don't actually answer my question. I'm not asking for the simple stuff. I'm asking for someone who understands general relativity to clear or confirm the GR stuff for me. Basically the parts that you get if you major in physics at a college.

Let me be brief this time: from the frame of reference of someone far away from the black hole, matter never actually enters the black hole. Time dilates more and more as it approaches the event horizon, until it basically is just stuck just outside the event horizon. It only actually enters the black hole in the infinite future.

Basically unless the black hole always existed in your frame of reference (hence my quip about the Schwarzschild radius), it never will. It will always be a FUTURE black hole.

Which leads me to: since the universe itself is not infinitely old, it can't have black holes that always existed. So it can only have FUTURE black holes.

Which leads me to my problem: so in OUR time there can't be any such thing as a black hole. We can only have FUTURE black holes. What we effectively have, in OUR frame of reference, is something that, well, effectively behaves kinda like a black hole from the outside, same gravity and lensing and all, but all (or at the least most) of its mass is just hanging just OUTSIDE the event horizon, instead of being inside it.

Now I'm not pushing that as the truth or anything. But I'd like someone who understands GR better than I do, to tell me if that conclusion is just me doing an ad-absurdum on myself :p
 
HansMustermann said:
Basically unless the black hole always existed in your frame of reference (hence my quip about the Schwarzschild radius), it never will. It will always be a FUTURE black hole.

Which leads me to: since the universe itself is not infinitely old, it can't have black holes that always existed. So it can only have FUTURE black holes.
Click to expand...

I think you are getting hung up on the concept of now and what it means for a singularity to exist. The singularity doesn't exist in our future, that's true. You're trying to connect a now outside the black hole with a now inside the black hole. Connecting two now's together in SR is already something that doesn't make 100% sense. Different observers will disagree. The space time of a black hole is so twisted that such a connection breaks down all together.

From the point of view beyond the event horizon things are of course different. The singularity is the only place that exists in the future.

Not sure if that's the direction you are going. The other issue is that you seem to be defining a black hole as an object with a singularity that exists "now". As discussed above, the question is a bit non-sensical when phrased that way. A black hole exists if an amount of matter/energy exists within it's own Schwarzschild radius (minus corrections for charge and spin) That's the actual definition of a black hole.

Of course, there are lots of unknowns related to the singularity itself and how general relativity and quantum mechanics interact.
 
RussDill said:
I think you are getting hung up on the concept of now and what it means for a singularity to exist. The singularity doesn't exist in our future, that's true. You're trying to connect a now outside the black hole with a now inside the black hole. Connecting two now's together in SR is already something that doesn't make 100% sense. Different observers will disagree. The space time of a black hole is so twisted that such a connection breaks down all together.

From the point of view beyond the event horizon things are of course different. The singularity is the only place that exists in the future.

Not sure if that's the direction you are going. The other issue is that you seem to be defining a black hole as an object with a singularity that exists "now". As discussed above, the question is a bit non-sensical when phrased that way. A black hole exists if an amount of matter/energy exists within it's own Schwarzschild radius (minus corrections for charge and spin) That's the actual definition of a black hole.

Of course, there are lots of unknowns related to the singularity itself and how general relativity and quantum mechanics interact.
Click to expand...

Well, this is starting to address my question, so I must thank you.

I am aware that different observers are at different points in time, as I mentioned in paragraph 8 of the first message in the thread. An observer may have already fallen into a black hole -- and yes, then it's eternally old from its point of view -- while for us he's still circling down the drain, and will never actually reach the event horizon.

But that's kinda my point. I'm talking only about our frame of reference, not about that of the black hole. I'm not trying to connect them. I'm just sticking to one frame: mine. (Verily, I say unto you, not only does the world revolve around me, but the whole universe does ;))

And in MY frame of reference, it seems to me like no black hole has formed yet. They're all future black holes. In MY frame of reference, all we have is some objects which behave mostly like a black hole from a distance (same gravity all) but has all the matter still outside the event horizon. In fact, it is effectively an empty shell around where the future black hole would be.

But on the other hand, everyone talks about black holes as already existing. In fact, there's a huge one at the centre of the galaxy, and a few thousand smaller ones around it.

You can probably see how that conflicts with my conclusion that in OUR frame of reference, not a single one has formed yet.

So I'm probably wrong and the rest of the world is right. Fine. Wouldn't be the first time. I'd just like someone to explain to me where I went wrong with it.
 
HansMustermann said:
Schwarzschild calculated that limit for an eternal black hole. It has always existed and it always will.
Click to expand...

Not quite.

The Schwarzchild metric works for any spherically symmetric, non-rotating, non-charged mass, in an asymptotically flat universe, outside the surface of the mass. Inside you need to shift to a different metric (depending on the radial mass distribution), but outside the metric is the same whether it's a black hole or a tennis ball. As long as it remains spherically symmetric, not rotating, and non-charged, the Schwarzchild metric applies outside the radius of the object. So you could have, for example, an mass that "breathes" (ie, the radius expands and contracts cyclically), and the Schwarzchild metric would still apply outside, and the changing mass distribution (since it's spherically symmetric throughout) wouldn't make any difference.

Now, if the object is NOT a black hole, then the Schwarzchild radius will be smaller than the radius of the object, so you stop using the metric before you reach that point. BUT, if the object in question shrinks enough (gravitational collapse), then eventually the radius of the object will become smaller than the Schwarzchild radius. Boom, it's a black hole. But the metric outside the initial radius never changes throughout this process.

And that's generally how black holes form. Don't think of it as acquiring more mass (and for stellar-mass black holes, they typically lose mass before they turn into black holes), think of it as the mass contracting until it hits that critical point.
 
Which just brings me to my question: would all that mass finish collapsing into a black hole, from the POV of an external observer, or you'd really have much less mass inside the Schwarzschild radius and a lot of it hovering frozen in time just outside it.

Let's take the smallest mass of a star remnant that would collapse into a black hole, which is IIRC about two solar masses and have a Schwarzschild radius of about 6km. Now very little of the mass of the black hole is going to already be within 6 km of the centre of the star. The rest has to collapse into that space.

So from the POV of an external observer, does it ever actually finish collapsing below 1.0 SR?
 
HansMustermann said:
Let's take the smallest mass of a star remnant that would collapse into a black hole, which is IIRC about two solar masses and have a Schwarzschild radius of about 6km. Now very little of the mass of the black hole is going to already be within 6 km of the centre of the star. The rest has to collapse into that space.
Click to expand...

That's a multi-part transition.

When a star begins life, it's mostly hydrogen. Heat from fusion reactions in the core keep the star from collapsing, and the density is low. Our sun has about the density of water.

When all that fuel burns out, heat isn't being generated in the core, so the mass will begin to collapse. As it shrinks, the gas compresses, heating up, and that heat will slow down the collapse. But since the star can also cool, that can only slow, not prevent, the collapse. As it turns into a white dwarf, another source of pressure emerges to help sustain the radius: electron degeneracy pressure. This is a quantum effect from the Fermi exclusion principle. The density of a typical white dwarf is about 1 million (106) times higher than our sun.

Now, there's something very important to realize about masses held up by degeneracy pressure. Unlike a normal star or planet, which has a larger radius if the mass is larger, a body held up by Fermi degeneracy has a smaller radius the larger the mass gets.

If the mass of the white dwarf is large enough, then the extreme pressure will actually drive electrons to fuse with protons to create neutrons. This relieves the electron degeneracy pressure, allowing for further collapse. As more neutrons are formed, you eventually get neutron degeneracy pressure holding up the now much-denser neutron star. The density of a neutron star is extreme, about 1017 times that of our sun. And again, the larger the mass of the neutron star, the smaller the equilibrium radius. If there's enough mass, then when enough electron-proton fusion happens, the star will collapse below its Schwarzchild radius. Then it's all over.

But before that final collapse, the star is already going to be incredibly dense, and much, much smaller than our sun.
 
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So most of the black hole's mass gets there before it actually generates an event horizon. And you don't see a naked singularity, because the event horizon forms in our present, not our future. The density goes up and up, information about events at the surface gets more and more redshifted, and then at the moment the mass crosses the Schwarzschild radius, >blip<, no more information comes out, and we're left with the infinitely attenuated infalling matter of the accretion disk around the event horizon.
 
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Well, let's look at the upper limit of neutron stars, right under that approximately 2 solar masses limit. Their radius is about twice their Schwarzschild radius. So while I'll grant that they're incredibly dense, they still only have about 1/8 of the mass inside the Schwarzschild radius when the final collapse begins. That's definitely not most of the mass already there, by any reasonable definition of "most".

BUT, as they continue to collapse, and the gravity increases, the time dillation starts to kick in.

So, from the point of view of an external observer, does that collapse ever finish? Does that collapsing neutron star ever actually gets all its mass inside its Schwarzschild radius?
 
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