Thermodynamics, stability and Hawking–Page transition of black holes from non-extensive statistical mechanics in quantum geometry

A semi-classical estimate for the q-parameter and decay time with Tsallis entropy of black holes in quantum geometry

“…The behaviors of the Gibbs free energy [1] G q for q > 1 is depicted in Fig. 4, We observe a minimum temperature T min q , at m = m min , no B H solution can exist below the minimal temperature and the space is filled with pure radiation.…”

“…we will use the entropy of Tsallis (we can view a method analogous to that described in ref. [1,14]) to generalize Boltzmann-Gibbs statistics. Using Eq.…”

“…On the basis of the Tsallis model with q > 1, we studied the properties of thermodynamic for the Schwarzschild B H, if 14is correct, one obtains the thermodynamic quantities following [1]:…”

“…In LQG the event horizon of BH is described by a 2Dsphere 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-extensive statistic in LQG are given in [1,14]. This work is a complementary to the previous article [1], where we used the ideas discussed in [14], to study some thermodynamic properties of the Schwarzschild-BH [15][16][17] meeting the non-extensive Tsallis entropy in the framework of the LQG [3] instead of the Bekenstein entropy.…”

“…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-extensive statistic in LQG are given in [1,14]. This work is a complementary to the previous article [1], where we used the ideas discussed in [14], to study some thermodynamic properties of the Schwarzschild-BH [15][16][17] meeting the non-extensive Tsallis entropy in the framework of the LQG [3] instead of the Bekenstein entropy. In the beginning, we will touch the problem of the stability of isolated BH when it is surrounded by a bath of thermal radiation, the BHs can also be in stable equilibrium with the thermal bath at a fixed temperature, on contrary to the standard Boltzmann description.…”