<p>Yes a threshold of concentrated mass/energy has to be exceeded. (by E=mc², Energy is Mass). How you achieve this is up to you!</p>
<p>The only proven way to concentrate enough mass into a sufficiently small volume is to collapse a large stellar core. The gravity of a core that is more than about 3 solar masses would compress the core enough to form a black hole.</p>
<p>But while that is the only proven way to make black holes, there are other speculative ways.  For example, in the early Universe, it is possible that random variations in density could have created black holes. These would be &quot;primordial black holes&quot;, they could be much smaller than 3 solar masses, or bigger.</p>
<p>There was even speculation that in high-energy collisions of particles, the energy concentration would be enough to form black holes.  It turns out that this doesn't happen at the energies of our particle colliders (but might happen in some cosmic ray collisions)</p>
<p>It doesn't matter how you get the mass/energy concentrated, if you can concentrate the mass enough, you will get a black hole. Particle colliders are a way of concentrating energy into a very small volume.</p>

CC BY-SA 4.0
2022-12-24T14:34:33.057Z
So black holes of sub-atomic sizes are currently theoretical and have never been observed ?
Demis
CC BY-SA 4.0
2022-12-24T14:44:17.980Z
They have never been observed. They weren't created in the LHC. The smallest observed black holes have a mass of about 4 suns.  The smallest theoretical mass that could be formed by a core collapse is only a little less than this.
James K
CC BY-SA 4.0
2022-12-26T03:24:55.437Z
@Demis Note that if you managed to make a black hole in an accelerator it would quite promptly go poof due to Hawking radiation.
Loren Pechtel
CC BY-SA 4.0
2022-12-24T10:36:16.480Z
2022-12-24T12:00:46.403Z
2022-12-24T12:00:46.403Z
James K
<p>Other answers have described how particles of very high energy could at least in theory collide to make tiny black holes. These energies are unlikely to happen in a mere TeV scale accelerator. However, the reason physicists considered black hole formation perhaps possible in particle accelerators was that gravity might change strength over small distances.</p>
<p>The idea is that spacetime has extra rolled up dimensions we normally do not observe (a standard concept from superstring theory). In <span class="math-container">$D$</span> dimensional space gravity declines as <span class="math-container">$1/r^{D-1}$</span>. On large scales spacetime is effectively 3-dimensional but below some distance (set by the size of the rolled up dimensions) it will effectively higher-dimensional, and <a href="https://arxiv.org/abs/hep-ph/9803315" rel="nofollow noreferrer">gravity will be stronger</a> since <span class="math-container">$1/r^{D-1}$</span> becomes bigger than <span class="math-container">$1/r^2$</span> for small <span class="math-container">$r$</span>. <a href="https://arxiv.org/abs/hep-ph/0106219" rel="nofollow noreferrer">This in turn allows black hole formation at lower energies</a>.</p>
<p>The fact that we do not observe black hole formation at the LHC is evidence against largish extra dimensions. (And, yes, there are <a href="https://arxiv.org/abs/0810.5515" rel="nofollow noreferrer">good reasons to think this is not just an anthropic selection effect against unlucky observers</a>.)</p>

CC BY-SA 4.0
2022-12-27T09:19:50.813Z
2022-12-27T09:19:50.813Z
Anders Sandberg
<p>The requirement to produce a &quot;black hole&quot; (at least of the simplest kind - a non-spinning, uncharged black hole) is just get a mass <span class="math-container">$M$</span> inside a radius <span class="math-container">$2GM/c^2$</span>. If <span class="math-container">$M$</span> is in kg and we use SI units, this means the mass has to be concentrated within a sphere of radius
<span class="math-container">$$ r &lt; 1.5 \times 10^{-27} M\ \ {\rm metres}\ .$$</span>
Obviously this is very small, unless <span class="math-container">$M$</span> is <em>very</em> big - a solar-mass black hole nneds to have that mass concentrated within 3 km.</p>
<p>However, you can also see from this simple equation that if <span class="math-container">$M$</span> is smaller than <span class="math-container">$10^{17}$</span> kg, then <span class="math-container">$r &lt; 1.5 \times 10^{-10}$</span> m, which can be described as &quot;sub-atomic&quot;.</p>
<p>The mass in question does not have to be in the form of matter. It can be in the form of energy (e.g. in the form of kinetic energy) and General Relativity makes no distinction between the two in terms of how the mass/energy influences spacetime. The equivalence between the two is <span class="math-container">$M = E/c^2$</span> and the inequality above could also be written
<span class="math-container">$$ r &lt; 1.7 \times 10^{-44}E\ \ {\rm metres}\ ,$$</span>
with <span class="math-container">$E$</span> in Joules. When two particles smash into each other in an accelerator (e.g. a particle and its anti-particle), then in the instant of collision, <em>all</em> their mass and energy is concentrated into a very small volume. In principle if the particle kinetic energies were high enough it might be possible to breach the condition above and make a black hole.</p>

CC BY-SA 4.0
2022-12-24T14:32:57.850Z
What do you mean "at least of a vanilla flavour" ?
Demis
CC BY-SA 4.0
2022-12-24T14:44:24.977Z
@Demis I mean a non-spinning, uncharged black hole.
ProfRob
CC BY-SA 4.0
2023-01-09T16:40:53.400Z
@Demis **Put simpler** it is the most simple kind/type of black hole :)  put more detailed; if needed:  it is as well as a part of the Schwarzschild Metric , which is a solution to the EinsteinFieldEquations
William Martens
CC BY-SA 4.0
2022-12-24T13:34:21.817Z
2023-01-09T17:58:11.180Z
2023-01-09T17:58:11.180Z
ProfRob
<p>I've heard of black holes forming in particle accelerators. This was a huge topic of discussion back in the early '00 with the grand experiment in CERN to prove the Higgs boson. Many people started expressing concerns about the formation of black holes. Of course scientists weren't concerned due to their very short existence.</p>
<p>But how can a black hole form from just some particle colliding with each other ?</p>
<p>As far as I know in order for a black hole to form a threshold of concentrated mass has to be exceeded.</p>

CC BY-SA 4.0
2022-12-24T18:58:15.270Z
The question is open whether it is even possible to create black holes that small.  If it were, dimensionless particles with mass would be black holes.  Plenty of interesting speculation, e.g. about [electron black holes](https://en.wikipedia.org/wiki/Black_hole_electron).  Still, this is about _quantum_ gravity, where nothing is quite settled.
RLWatkins
CC BY-SA 4.0
2022-12-27T23:59:40.877Z
You may enjoy playing with Viktor Toth's [Hawking radiation calculator](https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator).  FWIW, the proton (charge) radius is ~0.8768 fm. A BH with that Schwarzschild radius has a mass of ~590 million (metric) tons.
PM 2Ring
CC BY-SA 4.0
2023-01-09T16:36:16.687Z
black holes as far as I know, is *from* something that is compressed enough (not necessarily a star)  this is the Schwarzschild radius of a mass (if the mass is compressed below this radius- the black hole will form) and this radius is in some cases quite, small(correct me I'm wrong) $R_{s}=\frac{2GM}{c^{2}}$  ; where $R_{s}$ is the Schwarzschild radius and *G* is Newton's gravitational constant and  *M * is the object's mass, *c* is the speed of light.
William Martens
<black-hole>
How is it possible to have black holes in the sub-atomic scale?
Demis
# How is it possible to have black holes in the sub-atomic scale?

(Asked by: username_0 on 2022-12-24)

I've heard of black holes forming in particle accelerators. This was a huge topic of discussion back in the early '00 with the grand experiment in CERN to prove the Higgs boson. Many people started expressing concerns about the formation of black holes. Of course scientists weren't concerned due to their very short existence.

But how can a black hole form from just some particle colliding with each other ?

As far as I know in order for a black hole to form a threshold of concentrated mass has to be exceeded.

**Tags:** black-hole
> **Comments:**
> **username_1**: The question is open whether it is even possible to create black holes that small.  If it were, dimensionless particles with mass would be black holes.  Plenty of interesting speculation, e.g. about [electron black holes](https://en.wikipedia.org/wiki/Black_hole_electron).  Still, this is about _quantum_ gravity, where nothing is quite settled.  
> **username_2**: You may enjoy playing with Viktor Toth's [Hawking radiation calculator](https://www.vttoth.com/CMS/physics-notes/311-hawking-radiation-calculator).  FWIW, the proton (charge) radius is ~0.8768 fm. A BH with that Schwarzschild radius has a mass of ~590 million (metric) tons.  
> **username_3**: black holes as far as I know, is *from* something that is compressed enough (not necessarily a star)  this is the Schwarzschild radius of a mass (if the mass is compressed below this radius- the black hole will form) and this radius is in some cases quite, small(correct me I'm wrong) $R_{s}=\frac{2GM}{c^{2}}$  ; where $R_{s}$ is the Schwarzschild radius and *G* is Newton's gravitational constant and  *M * is the object's mass, *c* is the speed of light.  

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## 3 answers

### Answer by username_7 on 2022-12-24. Score: 12 | Accepted answer

The requirement to produce a "black hole" (at least of the simplest kind - a non-spinning, uncharged black hole) is just get a mass $M$ inside a radius $2GM/c^2$. If $M$ is in kg and we use SI units, this means the mass has to be concentrated within a sphere of radius
$$ r < 1.5 \times 10^{-27} M\ \ {\rm metres}\ .$$
Obviously this is very small, unless $M$ is *very* big - a solar-mass black hole nneds to have that mass concentrated within 3 km.

However, you can also see from this simple equation that if $M$ is smaller than $10^{17}$ kg, then $r < 1.5 \times 10^{-10}$ m, which can be described as "sub-atomic".

The mass in question does not have to be in the form of matter. It can be in the form of energy (e.g. in the form of kinetic energy) and General Relativity makes no distinction between the two in terms of how the mass/energy influences spacetime. The equivalence between the two is $M = E/c^2$ and the inequality above could also be written
$$ r < 1.7 \times 10^{-44}E\ \ {\rm metres}\ ,$$
with $E$ in Joules. When two particles smash into each other in an accelerator (e.g. a particle and its anti-particle), then in the instant of collision, *all* their mass and energy is concentrated into a very small volume. In principle if the particle kinetic energies were high enough it might be possible to breach the condition above and make a black hole.

> **Comments:**
> **username_0**: What do you mean "at least of a vanilla flavour" ?  
> **username_7**: @Demis I mean a non-spinning, uncharged black hole.  
> **username_3**: @Demis **Put simpler** it is the most simple kind/type of black hole :)  put more detailed; if needed:  it is as well as a part of the Schwarzschild Metric , which is a solution to the EinsteinFieldEquations  

---

### Answer by username_4 on 2022-12-24. Score: 7

Yes a threshold of concentrated mass/energy has to be exceeded. (by E=mc², Energy is Mass). How you achieve this is up to you!

The only proven way to concentrate enough mass into a sufficiently small volume is to collapse a large stellar core. The gravity of a core that is more than about 3 solar masses would compress the core enough to form a black hole.

But while that is the only proven way to make black holes, there are other speculative ways. For example, in the early Universe, it is possible that random variations in density could have created black holes. These would be "primordial black holes", they could be much smaller than 3 solar masses, or bigger.

There was even speculation that in high-energy collisions of particles, the energy concentration would be enough to form black holes. It turns out that this doesn't happen at the energies of our particle colliders (but might happen in some cosmic ray collisions)

It doesn't matter how you get the mass/energy concentrated, if you can concentrate the mass enough, you will get a black hole. Particle colliders are a way of concentrating energy into a very small volume.

> **Comments:**
> **username_0**: So black holes of sub-atomic sizes are currently theoretical and have never been observed ?  
> **username_4**: They have never been observed. They weren't created in the LHC. The smallest observed black holes have a mass of about 4 suns.  The smallest theoretical mass that could be formed by a core collapse is only a little less than this.  
> **username_5**: @Demis Note that if you managed to make a black hole in an accelerator it would quite promptly go poof due to Hawking radiation.  

---

### Answer by username_6 on 2022-12-27. Score: 4

Other answers have described how particles of very high energy could at least in theory collide to make tiny black holes. These energies are unlikely to happen in a mere TeV scale accelerator. However, the reason physicists considered black hole formation perhaps possible in particle accelerators was that gravity might change strength over small distances.

The idea is that spacetime has extra rolled up dimensions we normally do not observe (a standard concept from superstring theory). In $D$ dimensional space gravity declines as $1/r^{D-1}$. On large scales spacetime is effectively 3-dimensional but below some distance (set by the size of the rolled up dimensions) it will effectively higher-dimensional, and [gravity will be stronger](https://arxiv.org/abs/hep-ph/9803315) since $1/r^{D-1}$ becomes bigger than $1/r^2$ for small $r$. [This in turn allows black hole formation at lower energies](https://arxiv.org/abs/hep-ph/0106219).

The fact that we do not observe black hole formation at the LHC is evidence against largish extra dimensions. (And, yes, there are [good reasons to think this is not just an anthropic selection effect against unlucky observers](https://arxiv.org/abs/0810.5515).)


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