After an introduction to generalized uncertainty
principle(s), we study uncertainty relations as formulated in a crystal-like
universe, whose lattice spacing is of order of
Planck length. For Planckian energies, the uncertainty relation for
position and momenta has a lower bound equal to zero. Connections of this
result with 't Hooft's deterministic quantization proposal, and with double
special relativity are briefly presented. We then apply our formulae to
(micro) black holes, we derive a new mass-temperature
relation for Schwarzschild black holes, and we discuss the new thermodynamic
entropy and heat capacity.
In contrast to standard results based on Heisenberg and
stringy uncertainty relations, we obtain both a finite Hawking's temperature
and a zero rest-mass remnant at the end of the (micro) black hole evaporation.
[Ref.Paper: PRD 81, 084030 (2010). arXiv:0912.2253]