PRELUDIUM BIS 2 No DEC 2020/39/O/ST2/02323 (2021-2025).

Supervisor: Prof. Mariusz P. Dąbrowski, PhD student: Ilim Irfan Cimdiker.

We have demonstrated that for every nonextensive entropy, one should define an effective temperature (which we call equilibrium temperature) by utilizing the equilibrium condition, and that there is always an additive equilibrium entropy associated with this effective temperature. This is due to the fact that except for Bekenstein entropy, the **Hawking temperature is thermodynamically inconsistent with other nonextensive entropies**. We show the equilibrium requirement for the Tsallis–Cirto black hole entropy and demonstrate that the Bekenstein–Hawking entropy is the related equilibrium entropy, and the Hawking temperature is the associated equilibrium temperature for the Tsallis–Cirto black hole entropy.

- ''Generalized Uncertainty Principle and Nonextensive Entropies, Plenary talk at The 8th Conference of the Polish Society on Relativity, Warsaw, Poland, 19.09.2022 (M.P. Dąbrowski).

- Ilim Cimdiker, Mariusz P. Dąbrowski, Hussain Gohar, Equilibrium temperature for black holes with nonextensive entropy, European Physics Journal C 83, 169 (2023) (9 pages); eprint: 2208.04473

We have studied the effect of the generalized uncertainty principle (GUP) on nonextensive thermodynamics applied to black holes, as well as the sparsity of the radiation at different temperatures associated with nonextensive entropies such as: R\'enyi, Tsallis-Cirto, Kaniadakis, Sharma Mittal, and Barrow. We have shown that due to GUP corrections, the temperature and entropy have finite values, implying that **the final state of the black hole is a remnant at the end of the evaporation process and that the sparsity of the radiation for massless bosons at each temperature depends on the mass of the black hole**. We also find that GUP reduces the value of the sparsity profile for each case as compared to the sparsity parameter at Hawking temperature, which is always constant throughout the evaporation.

- Ilim Cimdiker, Mariusz P. Dąbrowski, Hussain Gohar, Generalized Uncertainty Principle Impact on Nonextensive Black Hole Thermodynamics, 2301.00609

- Ilim Cimdiker, Mariusz P. Dąbrowski, Hussain Gohar, Generalized Uncertainty Principle Impact on Nonextensive Black Hole Thermodynamics, Classical and Quantum Gravity (2023) (to be published).