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How could a micro black hole exist, when there is so little matter to produce the intense gravitational force required to crush matter to that extent? It takes the collapse of a supermassive star to provide that force. They make much bigger black holes. What is going to crush a little one even if it could have gravity concentrated enough to stay crushed?

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    $\begingroup$ There si no little or large matter, it depends on how close it is, that it, its density. If there is enough mass/energy density inside some small place, then it will become a black hole. It could be just 2 super energetic particles moving close to each other in opposite directions. $\endgroup$ Commented Jan 1 at 5:22
  • $\begingroup$ @PatoGalmarini what is the survival time of such a black hole? $\endgroup$
    – ProfRob
    Commented Jan 1 at 9:53
  • $\begingroup$ @ProfRob what is the total energy of the two particles at their center-of-mass frame? $\endgroup$
    – fraxinus
    Commented Jan 1 at 15:18
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    $\begingroup$ @fraxinus make them the most energetic particles ever detected. They need a rest mass energy of $>10^{26}$ J to survive for interesting amounts of time. $\endgroup$
    – ProfRob
    Commented Jan 1 at 15:43
  • $\begingroup$ @ProfRob I don't think that was the question, but I might be wrong. $\endgroup$ Commented Jan 1 at 18:57

5 Answers 5

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I'm guessing the issue here is not whether a small black hole is stable but rather what physical process could concentrate matter enough to form the small black in the first place.

And you are correct to question this because right now there are no known physical processes that could form small black holes. Any small black holes that exist now must have been created in the first few moments after the Big Bang when the density of the matter in the universe was much higher i.e. they are primordial black holes. Incidentally this sets a lower limit on the mass since any primordial black holes with a mass of less than $10^{11}~\textrm{kg}$ would have evaporated by now. This lower limit corresponds to a Schwarzschild radius of about $10^{-16}~\textrm{m}$ or slightly smaller than a proton so they are indeed small.

This area is somewhat speculative since we have only limited understanding of the very early stages of the universe, but the general idea is that there are several processes in the early evolution of the universe that would have been turbulent. This turbulence caused density fluctuations and formed small regions dense enough to form small black holes. Since there is no way to destroy a black hole (apart from waiting for it to evaporate) any small black holes formed in this way would still be with us.

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    $\begingroup$ I have to add that the experiments at Cern are looking at the possibility of micro black holes being created, according to some theories,home.cern/resources/faqs/will-cern-generate-black-hole $\endgroup$
    – anna v
    Commented Jan 1 at 9:14
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    $\begingroup$ when you say "would have evaporated by now" does this take into account how far away we could see a black hole evaporate and how long ago light we see from distant objects left them? $\endgroup$
    – Michael
    Commented Jan 1 at 16:17
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    $\begingroup$ @Michael a $<10^{11}$ kg black hole can radiate, at most, $< 9\times 10^{27}$ J over its entire lifetime. Only nearby (cosmologically speaking) evaporating mini black holes could possibly be detected. $\endgroup$
    – ProfRob
    Commented Jan 1 at 19:04
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Black hole doesn't require a lot of mass, it requires mass packed into an extremely small space. Any mass value $M$ has a corresponding quantity value called a Schwarzschild radius $r_s$. A black hole forms if the mass is packed into a region smaller than $r_s$.

The $r_s$ for the Sun is about 3 km. For the Earth, it is about 1 cm. Supernovae collapse are about the only macroscopic event energetic enough to pack matter into such dense state. But this could also be accomplished in principle by particle collisions, like cosmic rays hitting atoms in our atmosphere. The highest energy particles we detect have about the mass-energy of a fast pitch baseball, packed into the size of a nucleus. The Schwarzschild radius may be on the order of $\rm 10^{-28}$ m, but a high energy impact could potentially meet the proper conditions.

In fact, many cosmic rays are produced by supernovae, so in a sense these miniscule black holes would still be "formed by supernovae."

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    $\begingroup$ Any black hole that is still around now does require it to have had a threshold mass when formed. $\endgroup$
    – ProfRob
    Commented Jan 1 at 9:52
  • $\begingroup$ @ProfRob But it could have been born yesterday! $\endgroup$ Commented Jan 3 at 1:54
  • $\begingroup$ @LawnmowerMan then what mass/energy is required for that? $10^6$ kg = $10^{23}$ J = $10^{41}$ eV. Does that sound likely/possible that you can get two particles like that to collide? $\endgroup$
    – ProfRob
    Commented Jan 3 at 5:30
  • $\begingroup$ @ProfRob: I don't see why you're limiting yourself to two particles. You could have lots of particles. $\endgroup$ Commented Jan 3 at 18:47
  • $\begingroup$ I'm starting to question my answer, because the Schwartzchild radius of a proton is many orders of magnitude smaller than the proton radius, and it's hard to see how a quantum particle could be in any sense "localized" smaller than that. Is it the de Broglie wavelength that is the relevant length scale, meaning higher speed particles are more "localized"? But not in their own rest frame $\endgroup$
    – RC_23
    Commented Jan 4 at 0:16
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It's very unlikely we will find a primordial blackhole formed at the earliest times of the universe. This is because the background temperature was very high at that time and any blackhole formed will absorb the background radiation and (initially) increase in size and mass. Blackholes have the peculiar property that the more heat and energy they absorb, the colder they get. The colder they get, the less they radiate and the amount of radiation energy absorbed increases relative to the energy lost, so they continue to grow at an accelerating pace, even if they don't absorb massive particles.

However, if a primordial blackhole was initially tiny (e.g Plank mass) and somehow got isolated and only grew to something a bit less than the mass of the Moon by the time the universe had cooled sufficiently, then it could start losing mass and become a micro black hole in the current epoch. Once the background temperature has dropped below the temperature of the Moon sized blackhole, the blackhole starts to lose mass at a accelerating rate because it gets hotter as it loses mass, thus radiating even more than it absorbs from the background.

The highest energy extraterrestrial gamma particle ever detected, the so called Oh-My-God particle had an energy of about $50 J$. Compare that to the energy required to create a Planck mass black hole (about $ 2\times 10^9 J$). Even a head on collision between two of the highest gamma ray particles ever observed would not come close to the energy required to form a Planck mass blackhole. The energy of the OMG particle was some 40 million times that of the highest-energy protons that have been produced in any terrestrial particle accelerator, so the production of a Planck mass blackhole in a particle accelerator is extremely unlikely (to put it mildly).

However, there is an assumption here, that the smallest blackhole possible is a Planck mass blackhole. If that is not the case, then it is conceivable that micro black holes could be created in the collision of realistic energetic particles, but they would be extremely short lived.

Wikipedia gives the evaporation time of black hole due to Bekenstein/Hawking radiation as approximately $$t \approx 3.396 \times 10^{-16} \ \left(\frac{M}{kg}\right)^3 s$$ and for a Plank mass black hole the evaporation time would be $$t \approx 3.396 \times 10^{-16} \ \left(\frac{2.176 \times 10^{-8} Kg}{kg}\right)^3 s \approx 3.5 \times 10^{-39} s$$, assuming the the micro black hole does not absorb matter or background radiation in that time.

For a blackhole with 1/100 the Planck mass, the evaporation time would be $$t \approx 3.396 \times 10^{-16} \ \left(\frac{2.176 \times 10^{-10} Kg}{kg}\right)^3 s \approx 3.5 \times 10^{-45} s$$,

which is less than one Planck time interval. With the removal of the (possibly arbitrary) minimum mass restriction, it is possible that micro black holes are being produced all the time in collisions but evaporate almost immediately on a time scale that we cannot currently measure.

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    $\begingroup$ Just remember, black hole evaporation is still speculative physics, because Hawking radiation has not been confirmed to exist. $\endgroup$ Commented Jan 2 at 3:24
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    $\begingroup$ Does uncertainty set a minimum limit on the size of a black hole? $\endgroup$
    – EvilSnack
    Commented Jan 2 at 4:31
  • $\begingroup$ @EvilSnack I think uncertainty just limits our ability to measure exactly what happens at that scale. $\endgroup$
    – KDP
    Commented Jan 2 at 9:56
  • $\begingroup$ I don't know about energy, but Hawking radiation decreases as mass increases, which would make it look cooler (less hot), but I think that would be due to the increased gravity holding it in. For that reason I think very large black holes are ventually doomed by their ability to hold more energy than they radiate, even if it trickles in at only 1 or 2 deg. K heating them until the expansion force equals the gravitaional force. I think that's how the big bang occurred if there are other universes (as we know them (nodes)) out there to radiate bits of energy into it. $\endgroup$ Commented Jan 3 at 2:59
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    $\begingroup$ The first part of this answer is incorrect. Primordial black holes grow at a negligible rate in the early universe. Even though they are cold, the cross section for a particle to hit one is tiny (especially hot particles that can't be gravitationally focused). $\endgroup$
    – Sten
    Commented Jan 4 at 3:31
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The formation of a black hole is not dependent on mass it is dependent on density. According to General Relativity a black hole has three attributes, its mass, charge, and rotational velocity, In a simple Schwarzschild black hole you can calculate its Schwarzschild radius as $Rs = 2GM/c^2$. Neglecting charge and rotational velocity, when ANY mass is compressed within its own Schwarzschild radius it turns into a black hole.

To answer the second portion the smallest black hole we have ever observed is multiple times larger than the sun, theoretically very small nearly microscopic black holes could have been created by very dense pockets of matter in the seconds after the big bang. These primordial black holes being undiscovered so far could be partially thanks to hawking radiation from smaller black holes causing them to completely evaporate. Still a micro black hole is defined as under 1 solar mass which would take longer than 14 billion years to evaporate.

https://universe.nasa.gov/black-holes/types/#:~:text=Scientists%20theorize%20that%20primordial%20black,times%20more%20than%20the%20Sun's.

https://en.wikipedia.org/wiki/Schwarzschild_radius

https://www.nbcnews.com/id/wbna23904291

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    $\begingroup$ "The formation of a black hole is not dependent on mass it is dependent on density." -- it's not dependent on density either. It's dependent on M/r, which is closest to the Newtonian gravitational potential. $\endgroup$
    – Sten
    Commented Jan 4 at 3:41
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Gravity can be replaced by inertia. If the thin layer of the large sphere would "explode" producing a shower of high energy particles perpendicular to its surface, particles from the inner side will meet at the center, potentially reaching the critical density there.

Such a system obviously does not match any known astronomical object but we do not now what else we could find in the Universe.

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  • $\begingroup$ Which large sphere? What kind of explosion? $\endgroup$
    – PM 2Ring
    Commented Jan 4 at 17:51

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