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Is there some smallest amount of neutrinos needed to create a black hole?

Note that this question is not at all the same as the question here If a 1kg mass was accelerated close to the speed of light would it turn into a black hole?.

The other question asks if one particle alone can be turned into a black hole and this question asks how many particles is needed to form a black hole. Now obviously from the other question we can deduce that one neutrino alone is not enough to create black hole but the question still remains: can we create black holes out of two particles, three, more, how many are required?

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Molly Stewart-Gallus
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    Related - http://physics.stackexchange.com/q/3436/ – Xeren Narcy May 08 '15 at 01:17
  • While the linked duplicate specifically requests a 1kg mass, the answers there would be the same for this question here. – Kyle Kanos May 08 '15 at 02:04
  • @KyleKanos No, the answers would NOT be the same. These are different questions. The related question implies that more than one neutrino would be needed but doesn't answer how many would be needed. – Molly Stewart-Gallus May 08 '15 at 02:21
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    @StevenStewart-Gallus: It's the same in the sense that you are mistakenly believing that a fast moving particle can create a black hole. As to the other aspect of your question, do you know what the Schwarzschild radius is? – Kyle Kanos May 08 '15 at 02:47
  • As answered in the linked question, velocity is relative. It doesn't create mass that can form into a black hole. Energy turns into mass from the point of view of an observer, but not to the object itself - time dilation explains the discrepancy there. If you were to travel at .99999999999999999c you wouldn't notice any weight gain. You'd experience crashing into any particles very very fast and background radiation would be enormously blue-shifted, but you'd never create a black hole, any matter you pick up would appear normal, not massive, to you. – userLTK May 08 '15 at 02:49
  • @KyleKanos So you believe the smallest amount of neutrinos needed to create a black hole is two or what? – Molly Stewart-Gallus May 08 '15 at 03:14
  • @StevenStewart-Gallus: Take a few minutes to read about the Schwarzschild radius that I had mentioned in my previous comment. – Kyle Kanos May 08 '15 at 03:16

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The swarzchild radius is the distance a spherical mass has to be shrunk before it becomes a black hole. This is r = (2G/c²) m.

2G/c² is approximately equal to 1.48×10⁻²⁷ m/kg

Estimates for the mass of the neutrino vary somewhat. One estimate is from around 0.2 eV to 2 eV.

Picking 1eV for simplicity, the swarzchild radius is approximately 1.48×10⁻²⁷ m/kg times 2 times 1.783×10⁻³⁶ kg or around 5.3×10⁻⁶³ m.

Possibly if two neutrinos were brought within approximately 5.3×10⁻⁶³ m or smaller then they would form a black hole. There is no fully agreed upon theory of quantum gravity yet developed though. Also, one would have to bring those two neutrinos that close in the first place which might complicate things.

Note that the length is very much smaller than the Planck length (around 1.6×10⁻³⁵ m). So, I'm not sure if it is in fact possible to create a black hole using only two neutrinos because they would have to be put together so close that quantum effects dominate. Around 7×10²⁷ neutrinos would have to be put together before a swarzchild radius larger than the Planck length is reached. So, it may be that in fact there is a limit on the number of neutrinos needed to create a black hole and that limit is really, really, really, really large. Possibly.

Such a black hole would be extremely, extremely, extremely dense compared to typical black holes (which are formed from stars). Such a black hole would be as dense or denser than black holes formed at the start of the universe.

Molly Stewart-Gallus
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    There's 2 problems with this. One, I don't think anyone knows how gravity works at such tiny distances. There is no quantum theory of gravity so when you calculate a smaller than a quark or, smaller than a plank length black hole - you're calculating physical unknowns. Problem two, that kind of gravitational attraction only works if you assume Neutrinos have zero size. You can't get near 0 distance, and the necessary near infinite gravity between 2 quantum particles, cause they can't be pinned down. That's Heisenberg . Such a black hole, if it exists at all, would be unstable. – userLTK May 08 '15 at 03:47
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    As @userLTK pointed out above me, any black hole made out of neutrinos will be extremely unstable, and will quickly annihilate itself. – GRrocks May 08 '15 at 04:25
  • @GRrocks I am well aware that very small black holes decay very quickly via Hawking radiation. I still think it is interesting to ask what is the smallest amount of neutrinos needed to create a black hole even if it should decay shortly after creation. – Molly Stewart-Gallus May 08 '15 at 04:27
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    It is interesting for sure, my point was that GR isn't good enough to explain it. And your answer explains the rest, i guess. – GRrocks May 08 '15 at 04:35
  • You might want to look at the size of the very small. http://en.wikipedia.org/wiki/Orders_of_magnitude_%28length%29#Subatomic A 1 MeV neutrino is listed at 2x10-23rd. High energy Neutrinos 7x10-21st. Planck length or String theory, 10-35th. That's about the theoretical limit to smallness. 10-63rd is ten thousand trillion trillion times smaller than the strings of string theory, which have been criticized as being a very neat mathematical theory that won't ever be testable cause the strings are too small. 10-63 is small enough to effectively mean it can't happen. - er, I think. – userLTK May 08 '15 at 06:23