So..um...what if the Large Hadron Collider does create a tiny black hole

[appleciders]

@Chronos

If it doesn’t have an event horizon, it’s not a black hole. However, the event horizon will be extremely tiny-- It scales linearly with the mass.

The question about a black hole in the core of the Earth that’s large enough to remain stable is extremely interesting, but very difficult to answer, since although the black hole itself is simple, the core of the Earth is very messy indeed. But even in vacuum, a black hole of human mass would last roughly a second, which might be enough time to swallow a human mass of core.

@Chronos

Oh, and no matter what happens, we can already be completely, 100% confident that it won’t destroy the planet, since naturally-occurring cosmic rays have been observed with hundreds of times as much energy as anything the LHC can do. If particles of such an energy were going to destroy the Earth, they would have already done it.

No, don’t worry- I’m not one of the LHC worriers. I was just curious how big a hole it would take to actually matter.

[Uncle_Brother_Walker]

I think the question should be: “How much mass could a black hole mass if a black hole could mass mass?”
ba-dum-bump

[msmith537]

@Exapno_Mapcase

Weight of the earth = 1.31695337 × 10^25 pounds. Chronos said that a 226 pound black hole would last a second and devour 226 pounds. Therefore, assuming linearity, that black hole would take 5.8272273 × 10^22 seconds or 1.84657634 × 10^15 years. Too long to worry about.

Actually it would start out at 226 lbs. And then it would get bigger every time it bumped into something.

[Exapno_Mapcase]

@billfish678

Sure !

But someone better give him a little talk about his significant digit fetish

[homer simpson]Mmmm. Significant digits![/homer simpson}

Honest, officer, it wasn’t me. It was those Google-eyed guys over there!

@msmith537

Actually it would start out at 226 lbs. And then it would get bigger every time it bumped into something.

Yes. This is exactly what I assumed. Instead of evaporating, as in reality, I assumed it would grow by 226 pounds every second. I don’t think a larger black hole, weighing more to begin with, would bring in its own weight every second - the event horizon grows only in two dimensions - so this is a good deal for you. I was making the best possible case for your scenario on your own terms.

[Alex_Dubinsky]

@Exapno_Mapcase

assuming linearity

Newton: Hey, so i discovered this gravity thing.
Einstein: Oh yeah?
Newton: Yeah! I just have to figure out how fast apples fall down.
Einstein: Well just, you know, assume linearity.
Newton: Sweet.
Hawking: Hey, Einstein, maybe you can help me with this problem related to the intersection of general relativity and quantum mechanics that I have here…

[Washoe]

@msmith537

Well, it would be. If you find carrying around 226 lbs plus the mass of whatever you would need to contain the black hole so it doesn’t drop though the floor.

It doesn’t matter how damn much the container weighs. All the work you could do with 226 pounds of energy will more than make up for it. The bomb we dropped on Hiroshima liberated what—maybe a gram or two of energy?

[Washoe]

@Exapno_Mapcase

You’ll have plenty of time while your silly black hole does nothing.

Except evaporate.

Dammit, I was within the edit window. Coulda combined those two.

[Der_Trihs]

@Alex_Dubinsky

@Washoe

Let me see if I’ve got this straight. If you compress my fat ass down to a black hole, then I will go POOF one second later in a burst of 226 pounds (as of this morning) of Hawking radiation? This sounds like a nifty way to conveniently transport a lot of potential energy in a handy, compact form. Any way this could be used for rocket propulsion or anything else useful? Maybe we want to figure out a way to make some black holes?

Wait, how does this even work? I can extract work from your fat ass’s gravitational collapse. (Or, say, an ass large enough to collapse on its own.) And then you burst into light that I can extract more energy out of? Is this a free lunch?

No; it’s just that instead of those 226 pounds being in the form of fairly innocuous human flesh and bone, it radiates back out from the hole in the form of radiation. E=mc[sup]2[/sup] in action.

@Alex_Dubinsky

One thing I wanted to point out is that the Earth can’t just collapse into a [sufficiently large] black hole at its center. It’s got a bunch of rotational momentum, after all. It will have to radiate all of that off like a quazar before it can collapse.

Actually black holes rotate just fine; it just means that a slowly rotating planet would turn into a very quickly rotating hole.

[ZenBeam]

@Exapno_Mapcase

Weight of the earth = 1.31695337 × 10^25 pounds. Chronos said that a 226 pound black hole would last a second and devour 226 pounds. Therefore, assuming linearity, that black hole would take 5.8272273 × 10^22 seconds or 1.84657634 × 10^15 years. Too long to worry about.

Make the black hole a million times larger. That brings it down to 1.84657634 × 10^9 years. Still too big.

But even 1% of the earth’s mass would be an issue. That’s 1.84657634 × 10^7 years. Nope. Can’t worry yet.

There is no such thing as a small black hole that would make any difference in under geologic time.

Stop asking this question. Do a search for the 1.84657634 × 10^15 previous threads. Read them. You’ll have plenty of time while your silly black hole does nothing.

I think a bigger issue than how long it would take to eat the Earth is, how much mass could be converted to energy at the Earth’s core before there’d be noticeable effects due to all the extra core heat. I suspect this has an effect much sooner.

[Exapno_Mapcase]

@ZenBeam

I think a bigger issue than how long it would take to eat the Earth is, how much mass could be converted to energy at the Earth’s core before there’d be noticeable effects due to all the extra core heat. I suspect this has an effect much sooner.

A black hole is gravity. Period. It exerts a gravitational pull on matter. Once that matter goes through the event horizon, it just disappears from the rest of the universe. That’s it. There is no magic conversion to energy. It’s just gone. The entire point and definition of a black hole is that nothing escapes. A black hole is completely inert. It is, for want of a better term, black. There are effects at the event horizon for a number of reasons but at the sizes we’re talking about these would hardly compare to the surroundings, a ball of superheated iron under super pressures.

It’s possible that the total nothingness of the black hole might eventually show an effect because it would cool the surroundings, but what you postulate won’t happen.

[Grey]

His point is that the orbiting matter can shear across itself generating heat. You see it in gases being heated and emitting x-rays in galactic black holes. I suppose you could see it with liquid iron which might drive a stronger magnetic field and shed heat into the lithosphere driving more hot spots and volcanic activity. But that’s supposition on my part.

[billfish678]

@Exapno_Mapcase

[Yes. This is exactly what I assumed. Instead of evaporating, as in reality, I assumed it would grow by 226 pounds every second. I don’t think a larger black hole, weighing more to begin with, would bring in its own weight every second - the event horizon grows only in two dimensions - so this is a good deal for you. I was making the best possible case for your scenario on your own terms.

But, if a black hole size is linear with its mass, then its cross sectional area grows as a squared function. So, if its in a sea of molten iron, when its twice the mass, four times as many iron atoms are going to “bump” into to it per unit time right?

Note, I’ve given this about one minutes thought…

[msmith537]

@Exapno_Mapcase

A black hole is gravity. Period. It exerts a gravitational pull on matter. Once that matter goes through the event horizon, it just disappears from the rest of the universe. That’s it. There is no magic conversion to energy. It’s just gone. The entire point and definition of a black hole is that nothing escapes. A black hole is completely inert. It is, for want of a better term, black. There are effects at the event horizon for a number of reasons but at the sizes we’re talking about these would hardly compare to the surroundings, a ball of superheated iron under super pressures.

It’s possible that the total nothingness of the black hole might eventually show an effect because it would cool the surroundings, but what you postulate won’t happen.

Actually black holes emit a significant amount of x-rays, heat and other radiation at the event horizon when they are feeding. And once it gets to be a certain size, it will emit enough heat that it would start to raise the temperature of the Earth’s core.

[billfish678]

@msmith537

Actually black holes emit a significant amount of x-rays, heat and other radiation at the event horizon when they are feeding. And once it gets to be a certain size, it will emit enough heat that it would start to raise the temperature of the Earth’s core.

Thats a function of 3 things.

The amount of mass “falling” into the black hole.

The distance that mass falls.

The strength of the gravity of the black hole the mass is falling into.

For our theorized one poster mass small black hole inside the earth, all those values are a miniscule fraction of even a small normal black hole. Combine all three of these major reductions and the energy production is probably going to be nil.

[Chronos]

Quoth Exapno Mapcase:

Weight of the earth = 1.31695337 × 10^25 pounds. Chronos said that a 226 pound black hole would last a second and devour 226 pounds. Therefore, assuming linearity, that black hole would take 5.8272273 × 10^22 seconds or 1.84657634 × 10^15 years. Too long to worry about.

First of all, the one second figure was an order-of-magnitude estimate, so it could very easily be off by a factor of 10 either way, or even maybe a factor of 100. Second, the “eating its own weight every second” wasn’t even an estimate, but a WAG, and a weak lower bound of a WAG at that, based simply on the fact that a second is a really long time. Third, the accretion rate is probably proportional to the square of the mass, since as billfish678 pointed out, the cross-sectional area of the hole is proportional to the square of the mass.
Quoth Der Trihs:

Actually black holes rotate just fine; it just means that a slowly rotating planet would turn into a very quickly rotating hole.

Actually the Earth has far too much angular momentum to become a black hole: The Earth’s angular momentum factor is almost 900, while the same figure for a black hole can’t be greater than 1. Most likely, you’d end up with most of the mass of the Earth forming an accretion disk around the black hole, and very slowly falling in as it shed enough angular momentum to do so.

[Bryan_Ekers]

Geez, every time someone points out that a tiny black hole is harmless, somebody tries to redefine the situation so it looks dangerous again.
Talk about moving the hole-posts.

[ZenBeam]

@Exapno_Mapcase

A black hole is gravity. Period. It exerts a gravitational pull on matter. Once that matter goes through the event horizon, it just disappears from the rest of the universe. That’s it. There is no magic conversion to energy. It’s just gone. The entire point and definition of a black hole is that nothing escapes. A black hole is completely inert. It is, for want of a better term, black. There are effects at the event horizon for a number of reasons but at the sizes we’re talking about these would hardly compare to the surroundings, a ball of superheated iron under super pressures.

It’s possible that the total nothingness of the black hole might eventually show an effect because it would cool the surroundings, but what you postulate won’t happen.

Chronos wrote:

But even in vacuum, a black hole of human mass would last roughly a second, which might be enough time to swallow a human mass of core.

which I took to mean that the black hole would be swallowing and reradiating (through evaporation) a human mass every second. I thought you had made this assumption also in your calculations. In this case, the black hole doesn’t grow or shrink, and the Earth’s core has a very large heat source. I believe that that added heat would be a problem long before the Earth collapsing becomes a problem.

In reality, a human-sized black hole would evaporate almost instantly. Let’s calculate the lifetime of a 100 kg black hole: From here, a black hole’s lifetime varys by the cube of its mass, and a stellar mass black hole has a lifetime of 6.6 * 10[sup]74[/sup] seconds. The Sun is about 2 * 10[sup]30[/sup] kg, so a 100 kg black hole will evaporate (2 * 10[sup]28[/sup])[sup]3[/sup] = 8 * 10[sup]84[/sup] times faster, or 10[sup]-10[/sup] seconds.

[Grey]

@Bryan_Ekers

Geez, every time someone points out that a tiny black hole is harmless, somebody tries to redefine the situation so it looks dangerous again.
Talk about moving the hole-posts.

Round of applause!

[Alex_Dubinsky]

@Grey

His point is that the orbiting matter can shear across itself generating heat. You see it in gases being heated and emitting x-rays in galactic black holes. I suppose you could see it with liquid iron which might drive a stronger magnetic field and shed heat into the lithosphere driving more hot spots and volcanic activity. But that’s supposition on my part.

Additionally, since the black hole’s radius is so small and my rotational momentum fairly substantial, I would probably not fall into the black hole were the earth suddenly disappear and be replaced by one. I would orbit it. I would have to radiate off energy (after being heated by shear friction) before I can actually fall into it.

It should be pretty easy to calculate both the gravitational potential and rotational kinetic energy of the earth vs its center of gravity. I wonder how it would stack up against its total heat energy. Actually, perhaps it really wouldn’t be so great (that is, compared to its current total heat).

@Der Trihs

No; it’s just that instead of those 226 pounds being in the form of fairly innocuous human flesh and bone, it radiates back out from the hole in the form of radiation. E=mc2 in action.

I dunno. You can’t just turn matter into energy and go wheeee. Conservation of energy is one thing, but there’s entropy involved too. Is this really an entropy-raising reaction? If so, a tiny black hole would be quite the energy source.

[Chronos]

OK, I was just using numbers from memory, there, and it looks like I misremembered some numbers. Let me dig up the real figures…

First of all, that site’s figure for the lifetime of a stellar mass black hole is off. They’re calculating based just on radiation in photons, whereas most of the Hawking radiation seems to be in neutrinos, and the quantum mechanical statistics depends on the spins of the particles emitted. The correct figure for the lifespan of an astrophysical black hole (one of stellar mass or larger) is somewhere between 2.16e66 (M/M_sun)[sup]3[/sup] and 1.16e67 (M/M_sun)[sup]3[/sup] years.

However, you can’t just extrapolate that down to 100 kg, since the luminosity of a black hole depends on the number of kinds of particles that can be emitted, which in turn depends on the temperature of the hole. A stellar-mass black hole has a temperature of around 10[sup]-10[/sup] eV, which is only enough to emit photons, gravitons, and some neutrinos, whereas a human-mass hole would have a temperature of something like 10[sup]17[/sup] eV, plenty hot enough for the entire zoo of particles, probably hundreds of thousands of them.

So, yeah, I miscalculated-- We’re looking at ten to the minus twenty-something seconds for a human-mass hole. Now I’m wondering what exactly it was that I misremembered by that far off, to get the figure of ~1 second… I think I must have multiplied where I meant to divide, or something.