Nonextensive black hole entropy and quantum gravity effects at the last stages of evaporation

We analyze the generalized uncertainty principle (GUP) impact onto the nonextensive black hole thermodynamics by using R\'enyi entropy. We show that when introducing GUP effects, both R\'enyi entropy and temperature associated with black holes have finite values at the end of the evaporation process. We also study the sparsity of the radiation, associated with R\'enyi temperature, and compare it with the sparsity of Hawking radiation. Finally, we investigate GUP modifications to the sparsity of the radiation when GUP effects are introduced into R\'enyi temperature.