Determination of the Minimal Length by Microscopic Black Hole Temperature

TL;DR

This paper proposes a novel method to determine the minimal length scale, associated with the Planck length, by linking microscopic black hole formation, Hawking temperature, and quantum uncertainty principles.

Contribution

It introduces an original approach using Hawking temperature and relativistic kinetic energy to estimate the minimal length, extending previous classical kinetic energy models.

Findings

Minimal length estimated via black hole temperature.

Use of relativistic kinetic energy in minimal length derivation.

Connection between quantum uncertainty and black hole thermodynamics.

Abstract

Generalizing results of our previous work (where classical kinetic energy has been used) in this work (where ultra-relativistic kinetic energy is used) we suggest an original variant of the determination of minimal length (corresponding to Plank length) by formation of a microscopic (tiny) black hole. Like to some previous authors we use Heisenberg coordinate-momentum uncertainty relation, on the one hand. But, instead of metric fluctuation (obtained by second derivative in Einstein equations) that generalizes uncertainty relation by an additional term, used by previous authors, we use Hawking temperature of the black hole and standard Heisenberg coordinate-momentum uncertainty relation.