The discussions on the universal relation between corrections to entropy and the extremality of Schwarzschild-de Sitter black holes under the GUP and EUP

Abstract

We investigate the extremality relations by examining perturbative corrections to both the entropy of Schwarzschild-de Sitter black holes and their extremality bounds under the generalized uncertainty principle (GUP) and the extended uncertainty principle (EUP) respectively under the Nariai limit. We argue that the corrected uncertainty principles including GUP and EUP violate the validity of extremality relations because no matching condition can be imposed to support the Goon-Penco relation unless the influences from GUP and EUP disappear.