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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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Ms. Molly Stewart-Gallus
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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.

Ms. Molly Stewart-Gallus
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