No existence of black holes at LHC due to minimal length in quantum gravity

Abstract

We investigate the impact of the Generalized Uncertainty Principle (GUP), proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity Theories (DSR) on the production of mini black holes, and show that the minimum black hole mass is formed at energies higher than the energy scales of LHC which possibly agrees with the recent experimental results of LHC [1,2]

Minimal length, Friedmann equations and maximum density

“…Motivated again, by black hole physics, there is an another interesting connection between the Hawking radiation and the uncertainty principle [7][8][9][10][11][12][13] where the black hole can be modeled as n-dimensional sphere of size equal to twice of Schwarzschild radius. Since the Hawking radiation is a quantum process, one could assume that the emitted particles should obey the Heisenberg uncertainty relation.…”

“…By employing this GUP, it was found that the black hole thermodynamics quantities, such as temperature, and entropy are completely modified such that the end-point of Hawking radiation is not catastrophic anymore. This is because the GUP implies the existence of black hole remnants at which the specific heat vanishes and, therefore, the black hole cannot exchange heat with the surrounding space [7][8][9][10][11][12][13]. This means that GUP prevents the black hole from evaporating completely, just like the standard uncertainty principle prevents the hydrogen atom from collapsing.…”

“…It is worth mentioning that the GUP modifies, significantly, the entropy-area law as has been pointed out by several authors (see for example refs. [7,[11][12][13]). …”

“…We first review briefly the Generalized uncertainty principle (GUP) [14][15][16][17][18][19][20][21] and secondly we review its effect on the area-entropy law [7][8][9][10][11][12][13]. The existence of a minimum measurable length originates as an intriguing prediction of various frameworks of quantum gravity such as string theory [14] and black hole physics [15][16][17][18][19][20][21].…”

“…There has been investigations devoted to study the impact of GUP on the black hole thermodynamics and to the Bekenstein-Hawking (black hole) entropy (e.g., [7][8][9][10][11][12][13]). These studies are based on the argument that Hawking radiation is a quantum process and it should respect the uncertainty principle.…”