Area-law versus Rényi and Tsallis black hole entropies

Abstract: The R\'enyi and Tsallis entropies are discussed as possible alternatives to the Bekenstein-Hawking area-law entropy. It is pointed out how replacing the entropy notion, but not the Hawking temperature and the thermodynamical energy may render the whole black hole thermodynamics inconsistent. The possibility to relate the R\'enyi and Tsallis entropies with the quantum gravity corrected Bekenstein-Hawking entropy is discussed.