Uncertainty Relation on World Crystal and its Applications to Micro Black Holes

TL;DR

This paper introduces a generalized uncertainty principle within a 'world crystal' universe model, leading to novel predictions for micro black hole properties, including finite temperature and remnants, with implications for quantum gravity theories.

Contribution

It formulates a new uncertainty relation in a lattice universe at Planck scale and applies it to derive a distinctive mass-temperature relation for micro black holes.

Findings

Predicts finite Hawking temperature for micro black holes

Suggests existence of zero rest-mass remnants after evaporation

Connects world crystal model with quantum gravity frameworks

Abstract

We formulate generalized uncertainty relations in a crystal-like universe whose lattice spacing is of the order of Planck length -- "world crystal". In the particular case when energies lie near the border of the Brillouin zone, i.e., for Planckian energies, the uncertainty relation for position and momenta does not pose any lower bound on involved uncertainties. We apply our results to micro black holes physics, where we derive a new mass-temperature relation for Schwarzschild micro black holes. In contrast to standard results based on Heisenberg and stringy uncertainty relations, our mass-temperature formula predicts both a finite Hawking's temperature and a zero rest-mass remnant at the end of the micro black hole evaporation. We also briefly mention some connections of the world crystal paradigm with 't Hooft's quantization and double special relativity.