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Uncertainty relation on a world crystal and its applications to micro black holes
Open accessAbstract
We formulate generalized uncertainty relations in a crystal-like universe---a ``world crystal''---whose lattice spacing is of the order of Planck length. 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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Cites
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Cited by
Probing Planck-scale physics with quantum optics
Pikovski, I., Vanner, M. R., Aspelmeyer, M., Kim, M. S., & Brukner, Č. (2012) · Nature Physics · doi:10.1038/nphys2262 · Cited by 594
Teleparallel gravity: from theory to cosmology
Bahamonde, S., Dialektopoulos, K. F., Escamilla-Rivera, C., Farrugia, G., Gakis, V., Hendry, M., Hohmann, M., Levi Said, J., Mifsud, J., & Di Valentino, E. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac9cef · Cited by 503
Metadata
- Authors
- Jizba, P., Kleinert, H., & Scardigli, F.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2010-04-16
- Volume
- 81
- Issue
- 8
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2051574847
- Cited by
- 171
- References
- 13
- FWCI
- 4.39
- Type
- journal article
- Language
- en
- Open access
- green
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- Jizba, P., Kleinert, H., & Scardigli, F. (2010). Uncertainty relation on a world crystal and its applications to micro black holes. Physical Review D. https://doi.org/10.1103/physrevd.81.084030
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