Generalized uncertainty principle impact on nonextensive black hole thermodynamics

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 each nonextensive entropy, is investigated. We examine the Rényi, Tsallis–Cirto, Kaniadakis, Sharma Mittal, and Barrow entropies, temperatures, and heat capacities and show that, in each case, 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.