Micro black holes physics from world-crystal uncertainty principle. (English) Zbl 1219.83089
Fritzsch, H. (ed.) et al., Proceedings of the conference in honour of Murray Gell-Mann’s 80th birthday. Quantum mechanics, elementary particles, quantum cosmology and complexity, Singapore, February 24–26, 2010. Hackensack, NJ: World Scientific (ISBN 978-981-4335-60-7/hbk; 978-981-4338-62-2/pbk). 550-558 (2011).
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].
For the entire collection see [Zbl 1206.00045].
MSC:
83C57 | Black holes |
83F05 | Relativistic cosmology |
81S10 | Geometry and quantization, symplectic methods |
83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
80A10 | Classical and relativistic thermodynamics |
83E30 | String and superstring theories in gravitational theory |
83C47 | Methods of quantum field theory in general relativity and gravitational theory |
83A05 | Special relativity |
83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |