Summary: We formulate generalized uncertainty relations in a crystal-like universe whose lattice spacing is of order of Planck length – a “world crystal”. For energies near the border of the Brillouin zone, i.e., for Planckian energies, the uncertainty relation for position and momentum does not pose any lower bound. We apply these 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 black hole evaporation. We also briefly mention some connections of the world crystal paradigm with ’t Hooft’s quantization and double special relativity.
For the entire collection see [Zbl 1206.00045].