Can anybody explain how a black hole with mass of few dozens of atoms can gravitationally attract a significant amount of matter to grow? Is there some paper which quantitatively analyses how fast would such a tiny stable BH grow under some plausible circumstances?
If I take 1000 TeV, the expected energy of two colliding Pb ions on LHC, to be the mass of the produced BH (which is certainly a gross overkill), its classical Schwarzschild radius will be of order 10^-48 m. For comparison, the charge diameter of a proton is about 10^-15 m, the interatomic distances are of order 10^-10 m.
A black hole small enough that Hawking radiation is relevant is too small to be a danger to anything. As far as I can tell, a quite large black hole could sit at the center of the earth without doing anything noticeable. I think my calculation was that a 10 micron radius black hole at the center of the earth would have a doubling time of a billion years. That link is to Scott Aaronson’s blog where he asks that exact question. I recorded 10 microns there, but otherwise my calculations have been lost. Various people do similar calculations and seem to get similar numbers, but don’t all make the qualitative conclusion. One of the commenters linked to this paper, but I don’t recall extracting an answer from it.
Can anybody explain how a black hole with mass of few dozens of atoms can gravitationally attract a significant amount of matter to grow? Is there some paper which quantitatively analyses how fast would such a tiny stable BH grow under some plausible circumstances?
If I take 1000 TeV, the expected energy of two colliding Pb ions on LHC, to be the mass of the produced BH (which is certainly a gross overkill), its classical Schwarzschild radius will be of order 10^-48 m. For comparison, the charge diameter of a proton is about 10^-15 m, the interatomic distances are of order 10^-10 m.
A black hole small enough that Hawking radiation is relevant is too small to be a danger to anything. As far as I can tell, a quite large black hole could sit at the center of the earth without doing anything noticeable. I think my calculation was that a 10 micron radius black hole at the center of the earth would have a doubling time of a billion years. That link is to Scott Aaronson’s blog where he asks that exact question. I recorded 10 microns there, but otherwise my calculations have been lost. Various people do similar calculations and seem to get similar numbers, but don’t all make the qualitative conclusion. One of the commenters linked to this paper, but I don’t recall extracting an answer from it.