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 M_{min}, an approximate relationship between the q and gamma parameters of BHs can be found, (qapprox frac{sqrt{3}gamma }{pi ln 2}+1), which is remarkable approaching to q-parameters of cosmic ray spectra and quarks coalescing to hadrons in high energy.
Highlights
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 [3,4,5,6,7,8]
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
Summary
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 [3,4,5,6,7,8]. We will investigate a possible phase transitions in the system, we display a transition from the Hawking–Page and the change of the small-BH/large-BH of the first order, to the model of Schwarzschild BH in the anti-de Sitter (AdS) space These results confirm the resemblance between Tsallis-asymptotically flat in LQG and Boltzmann-AdS in the BH thermodynamics in the case q > 1.
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