Universality on thermodynamic relation with corrections in higher-dimensional de Sitter black holes

TL;DR

This paper extends the study of universal thermodynamic relations in higher-dimensional de Sitter black holes, incorporating angular momentum shifts and proposing a new universal framework relevant to quantum gravity.

Contribution

It introduces a more universal thermodynamic relation for rotating black holes and formulates a new conjecture linking shifted thermodynamic quantities across various backgrounds.

Findings

Universal extremality relation holds in higher dimensions.

Inclusion of angular momentum shift enhances universality.

Proposes a new framework connecting shifted thermodynamic quantities.

Abstract

In this study, the methodology proposed by Goon and Penco for investigating the universality on thermodynamic relations with corrections in de Sitter black holes is extended. A universal thermodynamic extremality relation, under consideration of the mass of the spacetime $M$ with various state parameters, proposed by Goon and Penco is investigated in higher dimensional spacetime, the established universal conclusions are not impacted by the convergence of energy from the coexistence region of two horizons to the point $N$ or $C$. Furthermore, by incorporating the shift of the angular momentum into our analysis, a more universal relation is derived, specifically applicable to rotating configurations. Notably, a novel conjecture is formulated that establishes a universal relationship framework connecting shifted thermodynamic quantities across arbitrary black hole backgrounds. These findings are expected to offer profound insights into the fundamental principles of quantum gravity.