# The Large Hadron Collider and Black Holes

Last week, I went to Switzerland and visited the LHC. I took a tour, and the guide told us that it is possible for black holes to appear in the LHC, but they will be so small, that they would evaporate away due to Hawking Radiation and there would be virtually no time for the black hole to "suck up" anything. I suddenly remembered something I read on this post that said a "a 100 tonne black hole would evaporate in 8.4×10−2 s, emitting approximately E=Mc2=9×1021 joules of energy as it does so – equivalent to more than a million megatons of TNT. I guess you could call this an explosion!"
If Mount Everest was condensed into a black hole, it would be smaller than a hydrogen atom. Mount Everest is 357 trillion pounds. 357 trillion pounds converted into energy would be a mind-boggling amount.
If a black hole formed in the LHC, wouldn't it completely annihilate it due to the spontaneous energy release due to Hawking Radiation? I'm new to the topic of Hawking Radiation, so I do not know if I have been misinformed in any way.

If a black hole formed in the LHC, wouldn't it completely annihilate it due to the spontaneous energy release due to Hawking Radiation?

The energy that the LHC reaches is 14 Tev: $$1$$ TeV is $$1.6e^{-7}$$ joule so there is no "million megatones" .

Even if they were created following some extra dimensional theories, they would have no time to accumulate and eat up matter around the detector and grow , as they evaporate very fast with Hawking radiation, which goes inversely proportional to mass.

Do we need to worry? Might these mini black holes start growing and, eventually, devour the whole earth? We should not worry about this. Even if you do not trust the calculations predicting a quick demise for such minuscule black holes, there is solid data to go by.

If black holes really form in high-energy particle collisions, they are also continuously created in the earth's atmosphere by the collision of Ultra High-Energy Cosmic Rays (UHECRs) with nuclei of oxygen, carbon, nitrogen and other elements present in the atmosphere.

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The collision energies for UHECRs can be enormous - some observations show energies of hundreds of TeV (hundreds of trillions of electron volts), which is much larger than the collision energies in particle collider experiments. And while the events with very high energy are exceedingly rare, this type of collision has been going on for literally billions of years, so an inordinate number of mini black holes would have formed. Since the earth has not (yet!) disappeared into one of these black holes, the much less massive man-made mini black holes should be quite safe.

For calculational details one can try this link.

I am not sure why there is this mania over black holes with the LHC. You can be certain there is no problem with this. In a given year a square kilometer receives a cosmic ray with energy up to $$10^7$$TeV or a million times the energy the LHC can muster. There has so far been no catastrophic event such as the occurrence of a black hole.

The concerns came in part from a thread in theoretical physics with extra large dimensions. The thinking was that in some dimensions beyond spacetime the scale may be much larger and thus at far lower energy. The idea emerged that maybe black holes could be formed at energy much lower than the Planck scale.

The Planck scale is a length where the de Broglie wavelength of a black hole equals half its perimeter length determined by the Schwarzschild radius. Then $$\lambda~=~\frac{2\pi\hbar}{Mc}$$ $$=~\pi r_s~=~\frac{2\pi GM}{c^2}.$$ Solving for the mass gives $$M~=~\sqrt{\hbar c/G}$$ $$\sim~2\times 10^{-8}kg$$. This mass is sort of the quantum unit of a quantum black hole. If such a black hole is generated by the collision of two particles it quickly ($$\sim~10^{-42}sec$$) scatters into other particles and radiation. This would occur at energy $$10^{15}$$ times the LHC energy. This is also associated with the Planck length that can be found as the Schwarzschild radius and this is $$1.6\times 10^{-35}m$$. However, the idea of large extra dimensions means this length, a scale near where Calabi-Yau manifold compactify, are much larger. So then a quantum black hole might then exist with a far smaller mass, and when it quantum evaporates by Hawking radiation it will then release far less energy.

The idea of large extra dimensions appears not to work, and some work with gravitational radiation indicates no expected loss of gravitational waves by leaking into these extra dimensions. The tour guide is right in that even if such a black hole were generated it would decay rapidly. Also if LHC were to generate a black hole it would have as much or less energy than the $$13$$TeV/nucleon of energy input to generate it.

There are analogues of black holes in QCD, where a gluon plasma has some black hole features. The work with heavy ions and the ALICE (A Large Ion Collider Experiment) detector, following up from RHIC have found some black hole characteristics which lends weight to gauge/gravity duality. These so called black holes can't suck anything up and are not really black holes.

• I am not sure why there is this mania over black holes with the LHC. You can be certain there is no problem with this. In a given year a square kilometer receives a cosmic ray with energy up to 107TeV or a million times the energy the LHC can muster. There has so far been no catastrophic event such as the occurrence of a black hole. This isn't a valid argument against the possibility of black hole production at TeV energies. They would have been traveling at close to $c$, so they would have flown through the earth without having time to accrete matter. – Ben Crowell Oct 19 '18 at 21:55