Making of Microscopic Black Holes

According to the theory of general relativity, all forms of energy, including momentum, generate gravity. As a result, it’s believed that gravity will become a significant factor at very high energies, specifically when the center of mass energies approach the Planck scale. At Planck energy, the collision of two particles can even create a microscopic black hole [71].

The four-dimensional Planck scale energy is $10^{19} \text{GeV}$ or $10^{28} \text{eV}$. According to the hoop conjecture given by Kip Thorne in 1972, if a large amount of matter and energy, represented by $E$, are compressed into a region, and if a hoop with proper circumference $2\pi R$ can fully encircle this matter in all directions, then a black hole will form if the resulting Schwarzschild radius (calculated as $R_s = \frac{2GE}{c^4}$) is larger than the value of $R$. The parameters used in this calculation include Newton’s constant ($G$) and the speed of light ($c$) [71]. Since the energy of the collision reaches a Planck scale, it can form a microscopic black hole. However, these microscopic black holes are not stable as they decay very rapidly through Hawking radiation [72], [73].

The particles that make up Hawking radiation are generated by the intense gravitational forces that exist around a black hole. These forces are strong enough to separate virtual particles, which are pairs of particles constantly popping in and out of existence in empty space. When one of these virtual particles is separated from its partner and falls into the black hole, the other particle is free to escape and create Hawking radiation. Thus through Hawking radiation, these micro black holes will decay instantaneously [74].

It is generally believed that miniature black holes decay by releasing elementary particles in the form of a spectrum of energy consistent with that of a black body [75]. The energy of these particles can be calculated through Hawking temperature. The energy $E$ of Hawking radiation is given by:

$E = \frac{\hbar c^3}{16 \pi G M},$

where $\hbar$ is the reduced Planck constant, $c$ is the speed of light, and $M$ is the mass of the black hole.

Sources & citation

https://www.researchgate.net/publication/369624131_Naked_Singularity_as_a_Possible_Source_of_Ultra-High_Energy_Cosmic_Rays