Can a High Enough Temperature Create a Black Hole?

Question

My very basic understanding of GR leads me to think that if a substance has a high enough temperature, it can transform into a black hole without a mass required to create a black hole.

The equation that I figure can express this is: $$\frac{2G(m+(stm)/c^2)}{c^2}=\text{Schwarzschild radius}$$ Where $G$ is the gravitational constant, $m$ is mass, $s$ is specific heat, $t$ is temperature, and $c$ is the speed of light. "$stm$" is equal to heat in joules and when it is divided by $c^2$ it is equal to mass. The masses are then added together, and the equation becomes identical to the Schwarzschild radius equation.

I'm sure there are much more advanced principles than what I am familiar with at such high heats, but is the premise of my logic sound? I doubt that energy from heat can translate so easily into mass, but I don't see the error in writing it so. Also, would this mean that there is a "maximum temperature" since anything that surpasses it would create a singularity?

Answer 1

You are asking about micro black holes.

Some hypotheses involving additional space dimensions predict that micro black holes could be formed at energies as low as the TeV range, which are available in particle accelerators such as the LHC (Large Hadron Collider). Popular concerns have then been raised over end-of-the-world scenarios (see Safety of particle collisions at the Large Hadron Collider). However, such quantum black holes would instantly evaporate, either totally or leaving only a very weakly interacting residue. Beside the theoretical arguments, the cosmic rays bombarding the Earth do not produce any damage, although they reach center of mass energies in the range of hundreds of TeV.

So it is a hypothesis at the frontier of research, theoretical and experimental.

I give a summary of BSM searches performed by the ATLAS and CMS experiments with an focus on heavy gauge bosons, extra dimensions and quantum black holes. The presented results use data collected during 2012 when the LHC operated at an center of mass energy of √s=8 TeV.