A semi-classical estimate for the q-parameter and decay time with Tsallis entropy of black holes in quantum geometry
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Letter
A semi-classical estimate for the q-parameter and decay time with Tsallis entropy of black holes in quantum geometry K. Mejrhita , R. Hajji Physics Department, Faculty of Science, Mohamed V University, Rabat, Morocco
Received: 20 September 2020 / Accepted: 31 October 2020 © The Author(s) 2020
Abstract In this letter, using the non-extensive entropy of Tsallis, we study some properties of the Schwarzschild black holes (BHs), based on the loop quantum gravity (LQG), some novel characteristics and results of the Schwarzschild BH can be obtained in Mejrhit and Ennadifi (Phys Lett B 794:45–49, 2019). Here we find that these findings are strikingly identical to ones obtained by Hawking and Page in anti-de Sitter space within the original of the Boltzmann entropy formula. By using the semi-classical estimate analysis on the energy at this minimum Mmin , an approximate relationship√between the q and γ parameters of BHs can be found, (q ≈ π ln3γ2 +1), which is remarkable approaching to q-parameters of cosmic ray spectra and quarks coalescing to hadrons in high energy.
1 Introduction Loop quantum gravity presents the spectrum of kinematic geometry operators such as the area operator and the volume operator [2]. It is a canonical quantification of general relativity within the framework of this formalism which leads to interesting applications of spin networks as the Hilbert space of the canonically quantized metric, the most fruitful implications that may arise from the application of LQG to BHs is to obtain a plausible explanation of BH thermodynamics based on non-extensive statistical mechanics taking into account strong gravitational couplings [3–8]. A comparative study of the results obtained with those based on Bekenstein–Hawking entropy shows the deep links between the entropy of BHs and their horizon surface, which clearly illustrates the underlying unity of the proposed cosmological models. In a similar way to that based on the Sharma–Mittal entropy formalism [9], which can be considered as a combination of Tsallis and Rényi entropy with the horizon sura e-mail:
face of the BH is not quantified, we have achieved important results on the thermodynamics of the BH in relation to its stability using Tsallis non-extensive statistical mechanics in the framework of quantum gravity theory. The LQG provides a guess of the microstates of a BH with the classical surface ( A), for the calculation of the entropy for BHs. The principal critique of this approach was the need to take a particular value of a free dimensionless parameter which is called the Barbero–Immirzi (BI) parameter (γ ) [10], to obtain the Bekenstein–Hawking entropy Horizon [11]. In LQG the event horizon of BH is described by a 2D– sphere which is a topological defects called punctures, where every edge of the global quantum geometry is represented with a spin carried by one puncture. In this work we will use Bekenstein–Hawking formula of the non-extensive Tsallis entropy [12,13] to develop the work done before, all motivations for the use of non-ext
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