Black hole thermodynamics is one of the most interesting recent discoveries of theoretical physics. The seminal connections between black holes and thermodynamics were initially made by Hawking and Bekenstein. Hawking discovered the thermal radiation from a black hole (BH) which was unexpected to the majority of specialists at that time. Bekenstein has realized that the area of the BH, resembles the concept of entropy and the gravity of the black hole is proportional to its temperature. The famous Bekenstein- Hawking equation combined gravity, quantum mechanics, and statistical mechanics together. In this research, for the first time, we investigate the thermodynamics properties of some types of black holes in the non-extensive approach of statistical mechanics. Also, we take advantage from non-extensive statistical mechanics and examine the critical behavior of the system. In such case, we obtain the first and second-order phase transition. We aim to study the thermodynamic properties of black holes in the concept of non-extensive statistics such as Tsaliss and Kaniadakis superstatistics and compare the results with the extensive statistics. We wish to investigate the conditions for the stability of the system, too. Furthermore, our purpose is to explore the critical bounds on the charged black holes, as well as study the issue of extremal and non-extremal black holes.
