Unobtanium shell around a black hole?

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Unobtanium shell around a black hole?

Postby swarmer » Sun Apr 20, 2008 8:01 pm UTC

I was reading the Wikipedia article on unobtanium, which is "is a humorous colloquialism that refers to any extremely rare, costly, or physically impossible material needed to fulfill a given design for a given application."

They gave an example of usage in an interesting thought experiment: "If one were to build an unobtainium shell around a black hole's event horizon, what would happen to the material piling up on it?"

What would happen? Or is it physically impossible for such a material to exist in this context?

My guess is that it would form a star. If so, it would have some really weird properties. Also, if the shell collapses when the star is already formed, that would be the coolest implosion ever.

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Re: Unobtanium shell around a black hole?

Postby phonon266737 » Sun Apr 20, 2008 8:12 pm UTC

I think it would just appear to be a really heavy ball, gravity wise. Light could bound off of it. Would it emit? I'm not sure, but in order for that to happen you'd expect it to be kinda hot. If it turned into a star (fusion), i guess the question is.. is plasma-phase unobtanium, solid?

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Re: Unobtanium shell around a black hole?

Postby TomBot » Sun Apr 20, 2008 8:39 pm UTC

If the shell was just outside the event horizon, then as more material piled on top, the event horizon would continue to expand. As soon as it encompassed the shell, the black hole would be indistinguishable from one without a shell.

While the shell is outside the event horizon, it may also need unobtanium-fueled thrusters to keep it centered.

Also, by constraining the speed of information transfer (and thus sound) to the speed of light, relativity puts an upper limit on the rigidity of materials. This might impose some lower limit on how close the shell can be to the black hole and not be crushed.

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Re: Unobtanium shell around a black hole?

Postby Robin S » Sun Apr 20, 2008 10:10 pm UTC

Gravitars are a related concept. The Wikipedia article doesn't describe what I thought it would, but it's a (possibly pseudoscientific) theory of an alternative to black holes - a hollow, infinitely dense spherical shell. I can't remember more details than that, but they featured in New Scientist a few years ago.
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Re: Unobtanium shell around a black hole?

Postby gmalivuk » Mon Apr 21, 2008 5:25 pm UTC

TomBot wrote:If the shell was just outside the event horizon, then as more material piled on top, the event horizon would continue to expand.

Even in relativity, I *think* the space inside a (hollow) spherically symmetric arrangement of matter is flat. And so adding matter to the shell won't initially have any effect on the size of the black hole inside.

However, it is true that at some point, the Schwarzschild radius of the shell and original black hole together will meet the outer radius of the shell itself, at which point you're correct: it will simply be a larger black hole with the mass of the original plus the shell.

I'm not sure what would happen before this point, though. (Or in the simpler related case where the shell is hollow the whole time.)
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Re: Unobtanium shell around a black hole?

Postby Yakk » Mon Apr 21, 2008 5:37 pm UTC

A black hole with the mass of the Earth, and an unobtanium weightless shell the radius of the Earth away, will have the surface gravity of the Earth.

Black holes don't suck any more than the same amount of mass not in a black hole does. Except with a black hole, you don't have the same amount of force pushing you away from it, and as you get closer and closer the gravity grad keeps on going up.
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Re: Unobtanium shell around a black hole?

Postby Jack.H » Tue Apr 22, 2008 5:52 am UTC

Yakk wrote:A black hole with the mass of the Earth, and an unobtanium weightless shell the radius of the Earth away, will have the surface gravity of the Earth.


So I guess subways are out of the question in unobtanium world... :D
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Re: Unobtanium shell around a black hole?

Postby Nimz » Tue Apr 22, 2008 10:01 am UTC

Jack.H wrote:
Yakk wrote:A black hole with the mass of the Earth, and an unobtanium weightless shell the radius of the Earth away, will have the surface gravity of the Earth.


So I guess subways are out of the question in unobtanium world... :D

Not necessarily. You'd need an unobtainium track for the subway to travel on, and the passengers would age less than if they had gone along the surface. This, in fact, would be one of the main advertising points: "Look younger: Take the subway!"

gmalivuk wrote:Even in relativity, I *think* the space inside a (hollow) spherically symmetric arrangement of matter is flat.

You're forgetting that in relativity you don't even need matter to make space curved. Any initial curvature, regardless of cause, creates gravity, which changes the curvature, which changes the gravity, which.... In short, flat space(time) is not required by relativity. A hollow, spherically symmetric arrangement of matter superimposed on a curved spacetime would not have a flat intereior.
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Re: Unobtanium shell around a black hole?

Postby Yakk » Tue Apr 22, 2008 1:20 pm UTC

No? Subways that just hang down from the unobtanium shell wouldn't have much problem, especially if they are as shallow as Earth-subways. If they fell apart, they'd fall down to the black hole (or, more likely, fall into an orbit inside the UnEarth).
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Re: Unobtanium shell around a black hole?

Postby swarmer » Tue Apr 22, 2008 9:29 pm UTC

So are black holes actually "holes"? Or is it just a really dense chunk of matter? If so, does matter just get squished onto it and the black hole gets bigger?

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Re: Unobtanium shell around a black hole?

Postby Master Gunner » Tue Apr 22, 2008 10:21 pm UTC

Really, really, dense chunks of matter. They're referred to as "holes" because things disappear into them. So yes, basically matter just keeps getting squished onto it and the black hole keeps getting bigger (in reality, due to time dilation, the matter wouldn't never actually reach the center of the black hole before the universe ceased to exist, but once something's past the event horizon, it really doesn't make any difference).

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Re: Unobtanium shell around a black hole?

Postby antonfire » Wed Apr 23, 2008 12:43 am UTC

By the way, it's easy to see that a static spherical shell has no gravity inside it in GR. The only spherically symmetric static vacuum solution to Einstein's equations is the Schwarzschild metric. The (empty) space inside of a static spherical shell of matter is indeed spherically symmetric. So, unless there's another black hole at the center, the metric is the Schwarzschild metric with r=0, i.e. flat space.
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Re: Unobtanium shell around a black hole?

Postby antonfire » Wed Apr 23, 2008 2:18 am UTC

Yes, that's under Newton's theory of gravity. The question is whether the same thing is true under Einstein's theory of gravity (General Relativity). The answer is yes.
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Re: Unobtanium shell around a black hole?

Postby Goemon » Wed Apr 23, 2008 6:08 am UTC

Actually if you start with a sphere of uniform density, and cut a spherical hole anywhere within it (even one off center), there will be zero gravitational field in the cavity according to Newton. (It's easiest to prove this by the rather bizarre technique of summing the graviational fields of the original solid sphere plus the "field" generated by a smaller uniform sphere with negative density located anywhere inside. The positive density plus negative density sum to zero = empty space = cavity. Weird method pointed out to me by someone a couple years ago - fun to play with :))

Not sure if the region in an off center cavity would be flat in relativistic mechanics, though I'm quite sure as antonfire said that it's flat inside a hollow sphere. Hmmm....

Also -

Seems to me that a thin shell located at the event horizon needs to be infinitely strong to keep from collapsing. Ok, slightly less than infinitely strong if it's a little bit above the horizon. But piling your old library books on top of it would mean it needs to be er... more than infinitely strong to support the extra weight. So even unobtainium would collapse... I guess...

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Re: Unobtanium shell around a black hole?

Postby Charlie! » Wed Apr 23, 2008 8:28 am UTC

Nah, "infinitely strong" just means that as it approaches the event horizon, there's a limit where the required strength goes to infinity. It doesn't mean that there's a definable strength that will keep it stable at the event horizon though - there isn't, at least not with relativity taken into account.
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Re: Unobtanium shell around a black hole?

Postby Xayma » Wed Apr 23, 2008 12:18 pm UTC

If you have it just larger than the event horizon then it will quickly become part of the black hole. If its a fair distance away, it will be the same as if you put it around anything else. (With possibly some more issues of stabilising it using any form of radiation to detect how centered it is that said you could get closer than normal). Other then that it probably depends on the material which is falling in and the conditions (if it has an accretion disc, it will probably heat up as the gas starts dragging along the surface etc).

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Re: Unobtanium shell around a black hole?

Postby Iv » Wed Apr 23, 2008 12:46 pm UTC

I don't see any reason why materials piling on the shell wouldn't start a star-like fusion reaction. Yes, it requires the shell to be big enough to still contain the hole after the matter piled, thus increasing its ratio.

It could be an intriguing SF plot device

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Re: Unobtanium shell around a black hole?

Postby evilbeanfiend » Wed Apr 23, 2008 12:49 pm UTC

it rather depends on the amount of available matter to fall on to the shell
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Re: Unobtanium shell around a black hole?

Postby Cyrion » Wed Apr 23, 2008 12:55 pm UTC

I know the hydrogen that would go in the accretion disk would heat a lot, but will that be enough to start fusion?

You need quite a lot of hydrogen to get a viable fusion. But I guess I underestimate the amount of hydrogen that would accumulate.
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Re: Unobtanium shell around a black hole?

Postby Iv » Wed Apr 23, 2008 1:32 pm UTC

Cyrion wrote:I know the hydrogen that would go in the accretion disk would heat a lot, but will that be enough to start fusion?

You need quite a lot of hydrogen to get a viable fusion. But I guess I underestimate the amount of hydrogen that would accumulate.


Considering that a typical black hole has a mass higher than a star, I would argue that the grvitational forces are far enough to start a fusion reaction

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Re: Unobtanium shell around a black hole?

Postby SpitValve » Wed Apr 23, 2008 2:29 pm UTC

Iv wrote:
Cyrion wrote:I know the hydrogen that would go in the accretion disk would heat a lot, but will that be enough to start fusion?

You need quite a lot of hydrogen to get a viable fusion. But I guess I underestimate the amount of hydrogen that would accumulate.


You get accretion flares in black holes and stuff. You build up enough hot dense hydrogen in the disc that it very quickly all fuses.

Remember these are damn hot discs - they're x-ray sources. That's how we detect the locations of possible black holes.

Iv wrote:Considering that a typical black hole has a mass higher than a star, I would argue that the grvitational forces are far enough to start a fusion reaction


Depends what you mean: A black hole is made from the leftover core after a star has gone supernova and flung out a crapload of gas. So a black hole starts off with less mass than the star that made it. But only massive stars make black holes, and most stars in the galaxy are little red dwarfs (smaller than the sun) so a typical black hole is more massive than a typical star.

Then you get the supermassive black holes in the centre of galaxies, which are simply bloody huge.

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Re: Unobtanium shell around a black hole?

Postby Yakk » Wed Apr 23, 2008 4:57 pm UTC

An interesting thought: would the unobtanium keep dark matter out of the black hole as well?
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Re: Unobtanium shell around a black hole?

Postby zenten » Wed Apr 23, 2008 5:08 pm UTC

Yakk wrote:An interesting thought: would the unobtanium keep dark matter out of the black hole as well?


For this purpose, sure. It's not like we actually know much of anything about it, besides the fact that it probably exists, and doesn't seem to create or interact with light/EM.

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Re: Unobtanium shell around a black hole?

Postby antonfire » Wed Apr 23, 2008 5:27 pm UTC

Goemon wrote:Actually if you start with a sphere of uniform density, and cut a spherical hole anywhere within it (even one off center), there will be zero gravitational field in the cavity according to Newton. (It's easiest to prove this by the rather bizarre technique of summing the graviational fields of the original solid sphere plus the "field" generated by a smaller uniform sphere with negative density located anywhere inside. The positive density plus negative density sum to zero = empty space = cavity.
Er, this seems wrong. Consider the gravitational field at the center of a spherical hole in a uniform sphere. The field due to the large positive density sphere pulls you towards the center.1 The field due to the smaller negative sphere does nothing. So, you get pulled toward the center.

1Remember that the gravitational field due to a sphere of uniform density is not zero inside the sphere. It's zero when you have spherical shells.
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Re: Unobtanium shell around a black hole?

Postby SpitValve » Wed Apr 23, 2008 5:38 pm UTC

yeah, I think you have to have your spherical hole in the centre of the constant density sphere.

For a counterexample, imagine a very small spherical hole just under the surface - the gravity there would be almost exactly the same as on the surface. People in submarines aren't weightless.

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Re: Unobtanium shell around a black hole?

Postby taby » Thu Apr 24, 2008 2:40 am UTC

Master Gunner wrote:Really, really, dense chunks of matter. They're referred to as "holes" because things disappear into them. So yes, basically matter just keeps getting squished onto it and the black hole keeps getting bigger (in reality, due to time dilation, the matter wouldn't never actually reach the center of the black hole before the universe ceased to exist, but once something's past the event horizon, it really doesn't make any difference).


The time to reach the central singularity is taken to be finite:

http://cosmology.berkeley.edu/Education/BHfaq.html#q9

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Re: Unobtanium shell around a black hole?

Postby Goemon » Fri Apr 25, 2008 7:07 am UTC

antonfire wrote:
Goemon wrote:Actually if you start with a sphere of uniform density, and cut a spherical hole anywhere within it (even one off center), there will be zero gravitational field in the cavity according to Newton. (It's easiest to prove this by the rather bizarre technique of summing the graviational fields of the original solid sphere plus the "field" generated by a smaller uniform sphere with negative density located anywhere inside. The positive density plus negative density sum to zero = empty space = cavity.
Er, this seems wrong. Consider the gravitational field at the center of a spherical hole in a uniform sphere. The field due to the large positive density sphere pulls you towards the center.1 The field due to the smaller negative sphere does nothing. So, you get pulled toward the center.

1Remember that the gravitational field due to a sphere of uniform density is not zero inside the sphere. It's zero when you have spherical shells.


You're right, because I meant to say "uniform", not "zero" :)

The field vector everywhere in the interior of the cavity is exactly the same magnitude and they're all perfectly parallel, so the region is essentially flat spacetime.

From an external viewpoint, all objects within the cavity accelerate at the same rate along perfectly parallel vectors - they don't converge toward the center of the larger solid sphere, and objects closer or farther from the center don't accelerate at different rates (no tidal forces).

Two objects initially at rest within the cavity maintain their relative seperation as they fall. Their situation is exactly equivalent to being in a spaceship accelerating in empty space. The cavity is intrinsically indistinguishable from empty, flat spacetime.

At least, until they crash into the wall of the cavity...

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Re: Unobtanium shell around a black hole?

Postby swarmer » Fri Apr 25, 2008 7:53 am UTC

If it did become a star, it would be fun to poke a hole in the shell and watch it suck itself up.

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Re: Unobtanium shell around a black hole?

Postby Nimz » Sun Apr 27, 2008 4:53 am UTC

Master Gunner wrote:Really, really, dense chunks of matter. They're referred to as "holes" because things disappear into them. So yes, basically matter just keeps getting squished onto it and the black hole keeps getting bigger (in reality, due to time dilation, the matter wouldn't never actually reach the center of the black hole before the universe ceased to exist, but once something's past the event horizon, it really doesn't make any difference).
[pedantic]The more massive the black hole, the less dense it is. Mass increases as r2, volume increases as r3.[/pedantic]

Spin a black hole and you can have yourself a stable negative energy orbit in the ergosphere. I wonder what would happen if you put the unobtainium shell (mostly?) inside the ergosphere with enough spin to have each part of the shell in one of those stable orbits.
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Re: Unobtanium shell around a black hole?

Postby SpitValve » Sun Apr 27, 2008 1:16 pm UTC

Nimz wrote:[pedantic]The more massive the black hole, the less dense it is. Mass increases as r2, volume increases as r3.[/pedantic]


yeah, there's confusion because "radius of the black hole" could refer to the radius of the event horizon or to the radius of the singularity (zero), and the definition of density depends on that. In the first case, it goes down as you get bigger. In the second case, it's always infinite.

It's more useful to define "radius of the black hole" as the radius of the event horizon, the Schwartzchild radius, because it is a more useful parameter that changes with different black holes, but this isn't what comes to mind straight away when people first hear the phrase "radius of a black hole" (or "density of a black hole, similarly).


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