# How is it possible to have black holes in the sub-atomic scale?

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.

• 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. Still, this is about quantum gravity, where nothing is quite settled. Commented Dec 24, 2022 at 18:58
• You may enjoy playing with Viktor Toth's 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. Commented Dec 27, 2022 at 23:59
• 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. Commented Jan 9, 2023 at 16:36

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.

• What do you mean "at least of a vanilla flavour" ? Commented Dec 24, 2022 at 14:32
• @Demis I mean a non-spinning, uncharged black hole. Commented Dec 24, 2022 at 14:44
• @Demis Such blackholes are known as Swarzchild Blackholes
– user47732
Commented Dec 30, 2022 at 12:50
• @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 Commented Jan 9, 2023 at 16:40

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.

• So black holes of sub-atomic sizes are currently theoretical and have never been observed ? Commented Dec 24, 2022 at 14:34
• 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. Commented Dec 24, 2022 at 14:44
• @Demis Note that if you managed to make a black hole in an accelerator it would quite promptly go poof due to Hawking radiation. Commented Dec 26, 2022 at 3:24

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 since $$1/r^{D-1}$$ becomes bigger than $$1/r^2$$ for small $$r$$. This in turn allows black hole formation at lower energies.

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.)

Yes, It is possible. Such a Black hole would be called a Micro Black Hole also known as Quantum Black Holes which are <1M☉, however if you want a black hole to be formed just moments after the Big bang it is going to be called an primordial black hole.

We can do a bit of math in order to calculate it:

So the mass energy equivalence equation is used ($$M=E/C^2$$) and in order to find the energy then check if it's in the range with the max created in the LHC is 13.7 TeV (LHC, CERN can go till 14 TeV) so the $$M$$ would be near to 1.5243 * 10^-16 kg with primordial black holes ranging from the Planck mass (21.764 micrograms) so it quickly becomes clear that it is possible.

Such a Black hole formed out of energy will be known as a Kugelblitz

In order for an object to become a black hole it has to be compressed/to be smaller than it's Schwarzschild radius

## $$R_{s}=\frac{2GM}{c^{2}},$$

where,

• $$R_{s}$$ = The Schwarzschild radius;
• $$G$$ = Isaac Newton's Gravitational constant;
• $$M$$ = The object's mass;
• $$c$$ = The speed of light.

Regardless of how you compress it (it's value would be 2.264×10^-43 meters), moreover if the collision produced a Kerr black hole instead of a Schwarzschild black hole i.e the black hole would have angular momentum then the Schwarzschild radius would get a bit smaller.

But don't worry (as specified in the question) it wouldn't devour the world because the Hawking radiation (1.533×10^64 watts meaning 1.706×10^47 kilograms per second) would make it evaporate extremely quickly and would have such tiny masses, the only danger would be the energy it emits.

footnotes

• Where does 1.5243 * 10^-16 kg come from? 14 TeV / c^2 ~= 2.5 × 10^-23 kg. (FWIW, the Google Calculator can do that calculation). Commented Dec 27, 2022 at 23:51
• @PM2Ring I used the 13.7 TeV value. Also thanks for telling that google calculator can also do it Since I only use Wolfram Alpha for Complex calculations like squaring the speed of light
– user47732
Commented Dec 28, 2022 at 5:05
• * It was 13.6 not 13.7 but anyways CERN can beat this record
– user47732
Commented Dec 28, 2022 at 5:21
• @WilliamMartens I meant the lower case $c$ to represent the speed of light, and Thank you for improving the answer
– user47732
Commented Jan 10, 2023 at 12:05
• Thank you, @WilliamMartens.
– user47732
Commented Jan 10, 2023 at 12:10