17
$\begingroup$

The first item is the basic question; the subsequent items build upon it if it's possible. If these need to be broken into separate questions, I can do that, but they're pretty tightly related.

  1. Is a non-rotating negatively-charged singularity small enough to be contained by a C₆₀ Buckyball theoretically possible?
  2. Would the charge repulsion of the carbon electrons be stronger than the gravitational attraction, keeping the singularity from consuming them?
  3. Is it theoretically possible for a singularity to be too small to absorb hadrons or even elementary particles?
  4. Anything this small would doubtless evaporate very quickly, but just how long could they last?

Thanks!

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ I think it all looks like an X & Y problem. Idea of getting canned BH isn't particularly good. Yeah, there's idea of something like that with antimatter, but it's already far-fetched. Another issue is that you shouldn't mix up concepts of singularity and black hole. BTW I think questions like that are more suitable for Physics.SE, or maybe Worldbuilding.SE - while the answer mentions, still quite big, primordial black holes, it's not like even smaller ones aren't hypothetically possible, but have more to do with physical speculation the astronomy. $\endgroup$
    – Mithoron
    Commented Mar 25, 2022 at 22:39

1 Answer 1

Reset to default
18
$\begingroup$

  1. A buckyball is about a nanometre ($10^{-9}$ m) across. If you limit the charge on the black hole to something like that of an electron or a few electrons, then this would mean the event horizon(s) of a charged, spinless, Reissner-Nordstrom black hole would be almost indistinguishable from that of a Schwarzschild black hole. The mass of this black hole would therefore be around $r_s c^2/2G \simeq 10^{18}$ kg. Yes, this is theoretically possible and maybe such black holes were produced during the big bang and are still around today.

  2. For Coulomb forces to outweigh gravitational forces then you need $$ \frac{Q^2}{4\pi \epsilon_0} > G M_{\rm BH}{m_C}\ .$$ In this case $Q \sim 10^{-18}$ Coulombs, $M_{\rm BH}\sim 10^{18}$ kg, $m_C = 12\times 1.67\times 10^{-27}$ kg. The LHS is $\sim 10^{-26}$ Nm$^2$ and the RHS is $\sim 10^{-18}$ Nm$^2$. So perhaps surprisingly, gravity will win and the buckyball will almost instantly be incorporated into the black hole.

  3. We don't have a theory governing the quantum behaviour of black holes. A singularity doesn't really have a size in a non-spinning black hole.

  4. A $10^{18}$ kg black hole would evaporate via Hawking radiation in about $10^{30}$ years.

Improve this answer
$\endgroup$
3
  • 1
    $\begingroup$ Thanks, @ProfRob, I was hoping you would answer. 😁 You're so very informative. So if I can get the RHS down, it's theoretically possible - but I'll have to do the math. I couldn't find anything to determine the inside radius of a Buckyball, not impacting the cabin electron shells. Wouldn't that matter? $\endgroup$
    – RoUS
    Commented Mar 24, 2022 at 20:41
  • $\begingroup$ "Yes, this is theoretically possible and maybe such black holes were produced during the big bang and are still around today." @user253751 $\endgroup$
    – ProfRob
    Commented Mar 25, 2022 at 10:07
  • 3
    $\begingroup$ Is there a reason you limited the charge to a few electrons? How would things change if you increased the charge to be sufficient for electromagnetism to win out over gravity? $\endgroup$
    – Michael
    Commented Mar 25, 2022 at 14:55

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .