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

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

2009-12-11

arxiv.org/abs/0912.2253v2

Phys.Rev.D81:084030,2010

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, 2 figures, latex4

Scientific paper

10.1103/PhysRevD.81.084030

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.

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