The title pretty much says it. How small could a black hole be? Either the event horizon, or the size of the mass itself. Both really.
There’s a wikipedia article on everything. Some people think they could get down into the quantum regime (this has never been observed), maybe even on the order of something you could produce in a particle accelerator (hence the scare about the LHC ending the world). If such a black hole is possible, current thought is that they would evaporate via Hawking radiation very quickly.
Well, the basic idea is that for any given mass you can figure its Schwarzschild radius. This is a radius that if you were to compress all the mass within it, it would form a black hole.
What the theoretical lower limit is on that, I dunno.
If I did the math right, a black hole of mass 228,000 kg would evaporate in a second, and have a radius of 3.39*10[sup]-22[/sup]. Evaporation time scales with the cube of mass, so as you get smaller, the black holes start to evaporate very quickly (a 228 kg black hole would last a nanosecond, for instance).
According to this Wiki entry on micro black holes, the minimum mass is limited by the Planck mass:
[QUOTE=Wikipedia]
Minimum mass of a black hole
In principle, a black hole can have any mass equal to or above the Planck mass (about 22 micrograms). To make a black hole, one must concentrate mass or energy sufficiently that the escape velocity from the region in which it is concentrated exceeds the speed of light. This condition gives the Schwarzschild radius, R = 2GM/c^2, where G is the gravitational constant and c is the speed of light, and M the mass of the black hole.
[/QUOTE]
radius of 3.39*10[sup]-22. Of what? meters? Miles? The diameter of the nucleus? There really isn’t a nucleus at that point of density I would think.
I think I understand why they might evaporate so quickly when they are small. Basically not enough gravity to keep it together?
I see info about stellar black holes that are about 30km in diameter. Also micro black holes at .1mm that ‘might’ be created by a created by a SHC. But what about golf ball black holes? Any way?
Sorry–that’s meters! And you’re right, there’s no nucleus or anything left at that point.
There’s enough gravity, almost by definition. There’s no easy way to explain why they evaporate. Quantum fluctuations near the event horizon are the enabler, but the basic argument for evaporation (Hawking radiation) is essentially thermodynamic in nature: black holes should have a temperature, and small black holes are really hot, and that mass/energy gets radiated away.
Sure. That’s a bit over two Earths of mass. It would take much longer than the age of the universe to evaporate. However, it would be essentially impossible to actually make such a black hole. A mass of that size will never collapse of its own accord. You can’t start small and work your way up due to Hawking radiation. And you can’t start big and work your way down since black holes can’t split apart.
There explicitly is enough gravity to keep it together. That’s what the calculation showed. Black holes are thought to evaporate via Hawking radiation, with smaller ones evaporating faster.
The ones that “might” be created by the LHC would not be anywhere close to .1 mm. They would have to be smaller than is really “possible” under currently-understood physics. It’s only if you invoke extra dimensions that they become theoretically possible at all, and even then they would still be expected to evaporate essentially instantaneously.
Yes, I saw the .1mm and thought that to be HUGE. So much for a quick Wiki.
I’ll need to learn more about Hawking radiation. I’ve heard of it of course, but never really looked at it.
OK. I understand that it takes tremendous mass to be able to compact to a black hole, and that a small one is theoretically possible. But to do so through evaporation due to Hawking radiation would take billions of years.
Then a golf ball sized black hole would be possible. Given enough time.
Are we talking about singularities here? No dimensions. And the ‘golf ball’ size is the event horizon?
Yes. The size of the black hole is referring to its event horizon as it wouldn’t be much of a black hole without a singularity at its center.
Way more than billions! The smallest mass that will collapse into a black hole naturally is called the Chandrasekhar limit, and is about 2.765x10[sup]30[/sup] kg. That mass would evaporate down to golf-ball size in about 56 million, trillion, trillion, trillion, trillion, trillion years.
Which happens to be about the time it takes to play through 18 holes.
As an aside: I did a project once on evaporation timescales, and found that the largest black holes we believe to exist, about a hundred billion times the mass of the Sun, would take something like 10^104 seconds to evaporate. It’s one of only two times I’ve ever encountered a number of over a googol in any real scientific context.
And we don’t know what the lower limit is on black hole size. This is one of the few cases where the Planck units are actually a good educated guess and not just a number pulled out of one’s posterior that’s better than anything else one might pull out of one’s posterior. But the physics of black hole evaporation must surely change radically at some point before that, and we don’t know how. Our extrapolations are useless here.
Don’t forget primordial black holes: they can be any size (above the planck-related minimums discussed above). Including golf ball sized.
But… Are there any black hole sized golf balls?
I’m glad to see this. It was always my understanding that the Plank units were cute, but no one had ever found that they meant anything physical at all despite claims that they were the largest or smallest possible somethings.
Well, in the specific case of a black hole, they do mean something, in that it’s somewhere in the vicinity of the Planck scale that we know our extrapolations definitely fail. Like, a black hole of about that mass should be radiating particles each of which has more energy than the hole itself does (there are some assorted dimensionless constants in that relation, too, but I can’t remember off the top of my head whether they’re bigger or smaller than 1).
But yeah, claims that, say, spacetime has Planck-sized “pixels”… Those are just a guess. Spacetime is probably quantized in some way or another, but we don’t know that the quantization takes the form of “pixels”, and even if it does, the Planck scale is just a guess as to their size, favored mostly just because nobody’s offered a better guess.
Holy shit. Spacetime might be anti-aliased voxels!
I await my Nobel Prize…
Right, on the gravity question, microscopic black holes by definition have an event horizon and a singularity at the center, so their gravitational strength at the EV is exactly that of massive black holes, and the theoretical density at the singularity infinite, or else they wouldn’t be black holes at all! The only difference between supermassive black holes and tiny microscopic ones is the gravitational gradient.
My understanding of Hawking radiation is painfully inadequate, but I still must object to the specific explanation about thermal radiation. By definition, nothing can escape from a black hole, so it can’t be written off quite that simply. I think the way it works – and here I’m paraphrasing from my shaky understanding of one of the Hawking lectures – is that Hawking discovered mathematically that a black hole should appear to emit radiation in accordance with the second law of thermodynamics as if it were a hot body with a temperature inversely proportional to its size. But what really happens has to do with quantum fluctuations in the vacuum outside the event horizon which creates virtual particle pairs.
Normally these virtual particles just annihilate each other in a process constantly going on in all empty space, but near a black hole the virtual particle with negative energy can fall into the hole and the positive-energy particle can escape to infinity. The universe has suddenly gained mass out of nowhere, but this is balanced by the negative-energy particle that has fallen into the black hole, causing the black hole to lose that infinitesimal amount of mass and to appear to have “radiated” a particle. But nothing has “really” escaped, which is what leads to all these interesting debates about the information-loss paradox.