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

TL;DR

This paper explores how quantum gravity-inspired modifications to uncertainty principles, GUP and EUP, affect the extremality conditions of Schwarzschild-de Sitter black holes, revealing violations of established relations unless these effects vanish.

Contribution

It demonstrates that GUP and EUP corrections disrupt the extremality relations of Schwarzschild-de Sitter black holes, challenging their universal applicability under quantum gravity effects.

Findings

GUP and EUP corrections violate extremality relations

No matching condition supports Goon-Penco relation with these corrections

Effects vanish when GUP and EUP influences disappear

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.