Does the energy of a particle collision affect the mass of the resultant Micro Black Hole?

Question

I know that some particle collisions energetic enough can temporarily create a Micro Black Hole before it evaporates. However, I am confused over whether the mass of the Black Hole is affected by the energy of the collision. Does the mass increase as the energy increases?

Answer 1

The only working theory of gravity that we have right now is Einstein's theory of general relativity (GR), which is a classical theory, i.e., it doesn't include quantum mechanics. In this theory, there is no minimum mass for a black hole, and for an isolated collision process surrounded by a lot of normal, approximately flat space, we have conservation of mass-energy. That is, mass and energy are not separately conserved. They are equivalent, $E=mc^2$, and you can trade one for the other. So according to GR, there is no fundamental reason why you can't collide one pool ball with another pool ball, at ordinary billiards-table speeds, and get a black hole. However, the dynamics of this process are not likely to work out, because ordinary material objects like pool balls won't compress anywhere near enough in such a collision.

Quantum-mechanically, there is the idea that everything not forbidden is compulsory (the totalitarian principle). That is, any process that isn't forbidden by a conservation law should probably happen, with some probability. We don't actually have a theory of quantum gravity, but if this general principle of quantum physics does hold in a theory of quantum gravity, then we should expect that there would be some probability for the pool balls to form a black hole. However, because we observe that it doesn't actually seem to happen, the probability is presumably incredibly small. Possibly in the very distant future of our universe, on time scales like $10^{10^{100}}$ years, such processes will result in the conversion of material objects into microscopic black holes. However, it's more likely that material objects will already have broken apart by then for more mundane reasons of thermodynamics.

The same considerations apply to collisions of fundamental particles. The probability of such a thing happening at an accelerator such as the LHC is believed to be too small to worry about. If you've read about this possibility and seen it described as something that could actually be a concern, that's probably in the context of theories involving large extra dimensions. I believe LHC data has now actually ruled out these theories (which nobody really expected were likely to be true even before the LHC was activated).

Since we don't have a theory of quantum gravity, it's hard to be very certain about other predictions besides these, but:

(1) Probably such black holes would evaporate on very short time scales, so the final result would actually be photons.

(2) Hand-wavy arguments seem to suggest that in a theory of quantum gravity, there is a minimum mass for black holes, which is on the order of the Planck mass, or about $10^{-8}$ kg. If so, then collisions at particle accelerators cannot make black holes at all, even with very low probabilities (assuming there are no large extra dimensions), because the energies are much smaller than the Planck mass times $c^2$.

Answer 2

I know that some particle collisions energetic enough can temporarily create a Micro Black Hole

These are highly theoretical. No micro black Holes have ever been observed and their existence is speculative.

By Einstein’s famous energy-mass relation,

$$m = \frac{E}{c^2}$$

we can see that the greater the energy will result in a greater mass. This would imply that the more energy is concentrated in particular collisions (protons) that could create microscopic black holes, then the more massive such an object would be.

But even if such objects were created, they would rapidly decay (in the form of Hawking radiation) losing their mass and energy.