Area-law versus Renyi and Tsallis black hole entropies

The Renyi 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 Renyi and Tsallis entropies with the quantum gravity corrected Bekenstein-Hawking entropy is discussed.

Automated summary

The Renyi and Tsallis entropies are discussed as potential alternatives to the Bekenstein-Hawking area-law entropy, with the importance of maintaining consistency with the notions of Hawking temperature and thermodynamical energy noted. The study also explores the possibility of relating the Renyi and Tsallis entropies to the quantum gravity corrected Bekenstein-Hawking entropy.