Loop quantum gravity Immirzi parameter and the Kaniadakis statistics

•Emergence of connection between the Loop Quantum Gravity Immirzi parameter and the area of a punctured surface.•Kaniadakis and Tsallis thermostatistics formalisms. In this letter we show that a possible connection between the LQG Immirzi parameter and the area of a punctured surface can emerge depe...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2019-01, Vol.118, p.307-310
Main Authors: Abreu, Everton M.C., Ananias Neto, Jorge, Mendes, Albert C.R., de Paula, Rodrigo M.
Format: Article
Language:English
Subjects:
Immirzi parameter
Kaniadakis statistics
Tsallis statistics
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Summary:•Emergence of connection between the Loop Quantum Gravity Immirzi parameter and the area of a punctured surface.•Kaniadakis and Tsallis thermostatistics formalisms. In this letter we show that a possible connection between the LQG Immirzi parameter and the area of a punctured surface can emerge depending on the thermostatistics theory previously chosen. Starting from the Boltzmann–Gibbs entropy, the Immirzi parameter can be reobtained. Using the Kaniadakis statistics, which is an important non-Gaussian statistics, we derive a new relation between the Immirzi parameter, the kappa parameter and the area of a punctured surface. After that, we compare our result with the Immirzi parameter previously obtained in the literature within the context of Tsallis’ statistics. We demonstrate in an exact way that the LQG Immirzi parameter can also be used to compare both Kaniadakis and Tsallis statics.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2018.11.033