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According to the Hoop Conjecture, if one can pack a sufficient amount of energy in a small enough region, black holes can be formed. The work on gravitational interaction between high energy particles indicate that classical black holes can be formed if the impact parameter is sufficiently small. An article by Xavier Calmet gives the estimate $b=3.2\mu$ where b is the impact parameter and $\mu$ is the center of mass energy.

So my question is - what determines how small the impact parameter can be? What prevents the formation of classical black holes (mass>>Planck mass) in LHC?

I know there was a lot of work about 'mini black holes' in the context of theories with large extra dimensions. I'm asking this for classical black holes in usual GR + standard model.

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It's all about energy. Planck mass sits on the value of $10^{17}$ TeV. In contrast, the LHC collide protons at a center-of-mass energy 13 TeV. It is way far from creating black holes with Planck mass. Unless you are staying in the context of large extra dimension scenarios, where Planck energy can be lowered to TeV scale, black hole production at LHC can become possible.

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  • $\begingroup$ yes, that's what one would expect. I'm a bit confused by papers such as this arxiv.org/abs/gr-qc/0201034 I am finding it difficult to see where energy scales enter here. $\endgroup$ Sep 28, 2016 at 16:32
  • $\begingroup$ The "classical" here means that the mass of the black hole >> lowered Planck energy. $\endgroup$
    – JamieBondi
    Sep 29, 2016 at 4:40
  • $\begingroup$ yes. I'm just not able to look at the calculation and see where energy scales enter. $\endgroup$ Sep 30, 2016 at 0:10

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