2013/09/17 by Tamás S. Biró, Viktor G. Czinner
Physics and Astronomy · #gr-qc #cond-mat.stat-mech #hep-ph #hep-th
paper · pdf · doi:10.1016/j.physletb.2013.09.032
published as Phys. Lett. B 726 (2013), pp. 861-865 · 5 pages, 1 figure, to be published in Phys. Lett. B. arXiv admin note: text overlap with arXiv:1011.3442
arxiv created 2013/09/17 · arxiv updated 2013/11/19
By regarding the Hawking-Bekenstein entropy of Schwarzschild black hole horizons as a non-extensive Tsallis entropy, its formal logarithm, the Rényi entropy, is considered. The resulting temperature - horizon-radius relation has the same form as the one obtained from a 3+1-dimensional black hole in anti-de Sitter space using the original entropy formula. In both cases the temperature has a minimum. A semi-classical estimate of the horizon radius at this minimum leads to a Bekenstein bound for the q-parameter in the Rényi entropy of micro black holes, (q >= 1 + 2/pi2), which is surprisingly close to fitted q-parameters of cosmic ray spectra and power-law distribution of quarks coalescing to hadrons in high energy accelerator experiments.