# Thread: Minimum Viable Size for a Black Hole?

1. ## Minimum Viable Size for a Black Hole?

Some years ago, the press reported worries that the Large Hadron Collider could generate a black hole. People at CERN actually considered this possibility, and said that a micro-black hole "would disintegrate rapidly, in around 10^-27 seconds". They would have been able to track its existence, and the data would have been an important step towards new knowledge and unknown possibilities.

Today I read that a black hole the size of a dime would need as much mass as the whole planet Earth. So how much mass do I need for a black hole that won't disappear for a few hours? What for one that will last as long as, let's say, a star (if that's possible for black holes)?

2. ## Re: Minimum Viable Size for a Black Hole?

According to them, 2/3 the size of the moon to sustain itself but it can't be generated by masses less than larger than the sun.

3. ## Re: Minimum Viable Size for a Black Hole?

The thing is, the acceleration toward the eruption of Hawking radiation is exponential. A black hole would appear stable until it was almost small enough to begin erupting, then it would be gone in a titanic blast. As I understand it, it would be the whole mass as e=mc^2, which is to say much more than the biggest nuclear bomb ever made.

4. ## Re: Minimum Viable Size for a Black Hole?

Theoretically once a black hole has the mass equal to the Planck mass it wouldn't be able to "evaporate" anymore since the radiating particle would need to have the mass energy equivalent of the Planck mass. The size would be the Planck length. It would be stable like this forever, and too small to actually ever absorb any energy (and if it did, just evaporate that again).
This is because the hawkins radiation emitted from a black hole needs to have a wavelength equal to the diameter of a black hole, so big ones emit low energy waves, smaller ones emit higher energy waves.

The sweet spot between "not radiating too fast" and "not radiating fast enough" seems to be around 606,000 metric tons if you want to use the Hawkins Radiation for something. It would be about 0.001 femtometer in diameter. (much smaller than an atom, the nucleus of an hydrogen atom is 1.7566 femtometer)
Source: https://en.wikipedia.org/wiki/Black_hole_starship

5. ## Re: Minimum Viable Size for a Black Hole?

Originally Posted by Tvtyrant
but it can't be generated by masses less than larger than the sun.
I think it could if they were already very dense and smashed together at relativistic speeds

6. ## Re: Minimum Viable Size for a Black Hole?

Originally Posted by Mastikator
Theoretically once a black hole has the mass equal to the Planck mass it wouldn't be able to "evaporate" anymore since the radiating particle would need to have the mass energy equivalent of the Planck mass. The size would be the Planck length. It would be stable like this forever, and too small to actually ever absorb any energy (and if it did, just evaporate that again).
This is because the hawkins radiation emitted from a black hole needs to have a wavelength equal to the diameter of a black hole, so big ones emit low energy waves, smaller ones emit higher energy waves.
Black holes can radiate particles larger than themselves.

As the practical escapes, it becomes redshifted, increasing it's wavelength.
Originally Posted by Bohandas
I think it could if they were already very dense and smashed together at relativistic speeds
I think TvTyrant meant generated naturally.

7. ## Re: Minimum Viable Size for a Black Hole?

Black holes can radiate particles larger than themselves.

As the practical escapes, it becomes redshifted, increasing it's wavelength.
I think TvTyrant meant generated naturally.
Right when the particle appears it would be a photon and have the energy and size of the black hole it is escaping from. This photon would a) be a Kugelblitz and b) evaporate the black hole completely. The result would be that the black hole has just moved one Planck length to the side.

8. ## Re: Minimum Viable Size for a Black Hole?

Originally Posted by Mastikator
Right when the particle appears it would be a photon and have the energy and size of the black hole it is escaping from. This photon would a) be a Kugelblitz and b) evaporate the black hole completely. The result would be that the black hole has just moved one Planck length to the side.
There a few problems with this.

First, there is no "right when the particle appears". The particle is virtual before it escapes. Virtual particles don't have energy the same way real particles do (which is to say, you can't use wavelength to determine their energy) . The particle doesn't become real until it's well away from the event horizon. The source of the virtual particle isn't even the event horizon, it's region of space that that ends in an event horizon; there is a pair of virtual particles outside the horizon (possibly bigger than the black hole) and one of two on falls in.

Second, you're ignoring potential energy. As accounted by the distant observer, that particle doesn't change it's total energy during it's journey. At infinity, the photon has zero energy. Infinitely close to the event horizon, the photon would have negatively infinite potential energy.

9. ## Re: Minimum Viable Size for a Black Hole?

Originally Posted by Mastikator
Theoretically once a black hole has the mass equal to the Planck mass it wouldn't be able to "evaporate" anymore since the radiating particle would need to have the mass energy equivalent of the Planck mass. The size would be the Planck length. It would be stable like this forever, and too small to actually ever absorb any energy (and if it did, just evaporate that again).
This is because the hawkins radiation emitted from a black hole needs to have a wavelength equal to the diameter of a black hole, so big ones emit low energy waves, smaller ones emit higher energy waves.

The sweet spot between "not radiating too fast" and "not radiating fast enough" seems to be around 606,000 metric tons if you want to use the Hawkins Radiation for something. It would be about 0.001 femtometer in diameter. (much smaller than an atom, the nucleus of an hydrogen atom is 1.7566 femtometer)
Source: https://en.wikipedia.org/wiki/Black_hole_starship
Would it be possible to extract further energy from the planck black hole by lifting its energy just above planck mass?

10. ## Re: Minimum Viable Size for a Black Hole?

All the energy you could possibly get out would be identical to the energy you put in.

11. ## Re: Minimum Viable Size for a Black Hole?

Originally Posted by Yora
All the energy you could possibly get out would be identical to the energy you put in.
Why? If the black hole is at .8 h (h being planck mass), and you put it up to, say 1.2 h, couldn't it then radiate away h to end up at .2 h?

12. ## Re: Minimum Viable Size for a Black Hole?

If that is the case, the energy you gain would literally be one of the smallest possible amounts amounts you'd ever get. Probably get a lot more energy from collecting the Cosmic Microwave Background.

13. ## Re: Minimum Viable Size for a Black Hole?

Originally Posted by Rydiro
Would it be possible to extract further energy from the planck black hole by lifting its energy just above planck mass?
It would be virtually impossible to add any energy to it, the cross-hair is literally the smallest meaningful length. The uncertainty principle says no.

It's also possible that no such black hole actually exists, it would have to been created in the big bang. AFAIK there's no evidence that they exist. A stellar mass black hole wouldn't become this light, a) the universe isn't old enough and b) it would gain much more energy just from the CBR than it would lose to Hawkins radiation.

14. ## Re: Minimum Viable Size for a Black Hole?

Quoth Mastikator:

Theoretically once a black hole has the mass equal to the Planck mass it wouldn't be able to "evaporate" anymore since the radiating particle would need to have the mass energy equivalent of the Planck mass. The size would be the Planck length. It would be stable like this forever, and too small to actually ever absorb any energy (and if it did, just evaporate that again).
It's more accurate to say that our current theories concerning black holes break down in the vicinity of the Planck mass, and thus we have no idea how such a hole would behave. For that matter, it's quite possible that our theories break down long before that point, but we're absolutely certain that they break down by then.

And while there's no known mechanism in the current Universe that could produce black holes smaller than a few times the mass of the Sun, it's quite possible that smaller holes might have been formed during the very early stages of the Universe, and some of those might still be around. And of course, it's also possible that there are mechanisms in the current Universe that we don't know of. So it would be very exciting, but no great surprise, to discover black holes of sub-stellar size.

15. ## Re: Minimum Viable Size for a Black Hole?

Originally Posted by Yora
If that is the case, the energy you gain would literally be one of the smallest possible amounts amounts you'd ever get. Probably get a lot more energy from collecting the Cosmic Microwave Background.
A quick application of E=mc˛ gives about 180 000 000 000 Joule for one planck mass, if I'm not mistaken.
Which would power a fridge for four years.
Sure, small on an industrial scale, let alone on an astronomical. But pretty sure beats the CMB.

16. ## Re: Minimum Viable Size for a Black Hole?

Originally Posted by Rydiro
A quick application of E=mc˛ gives about 180 000 000 000 Joule for one planck mass, if I'm not mistaken.
That looks high to me. They're expecting the emissions from any micro-blackholes produced in the LHC to be containable, which I don't think that would be.

17. ## Re: Minimum Viable Size for a Black Hole?

Originally Posted by Rydiro
A quick application of E=mc˛ gives about 180 000 000 000 Joule for one planck mass, if I'm not mistaken.
Which would power a fridge for four years.
Sure, small on an industrial scale, let alone on an astronomical. But pretty sure beats the CMB.
The Plank length is on the order of 10-35 meters. What's the order of a plank mass in grams? I confess I do not know.

E = m c2 => m = E/c2

c = 299,792,458 m/s.

c2 = 8.98755 x 1016 m2/s2 ~ 1.0 x 1017 m2/s2

180 billion joules is roughly 2.0 x 1011 kg m2/s2

m = (2.0 x 1011 kg m2/s2) / (1.0 x 1017 m2/s2)

The m2/s2 cancel out, and you're left with 2 x 10-6 kg. Or about 2 mg. I'm... pretty sure that's a good bit heavier than a Plank mass.

18. ## Re: Minimum Viable Size for a Black Hole?

Originally Posted by Lord Torath
Or about 2 mg. I'm... pretty sure that's a good bit heavier than a Plank mass.
Yeah, I was off by a factor of 100. Planck mass is 20 micro grams. I did get that right, but was off on c by a factor of 10.
Guess you can run that 1000 Watt fridge just for some weeks.

19. ## Re: Minimum Viable Size for a Black Hole?

Our current understanding of physics would not allow for the LHC to produce black holes. Which would mean that if it did produce black holes, that would be a sign that our current understanding was incomplete. But in any event, any black hole (or in fact, anything at all) produced by the LHC would have a mass much, much lower than the Planck mass. The only energy you'll ever get out of anything produced in a particle accelerator is the energy you put in, which won't be much.

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