Thermodynamic Extremality in Power-law AdS Black Holes A Universal Perspective

TL;DR

This paper explores the universal thermodynamic relation proposed by Goon and Penco across various power-law AdS black holes, demonstrating its robustness and universality through analytical and perturbative methods.

Contribution

It provides the first comprehensive analysis confirming the universality of the Goon-Penco relation in diverse power-law black hole models.

Findings

The GP relation holds consistently across Power-Maxwell, Power-Yang-Mills, and Maxwell-Power-Yang-Mills black holes.

Perturbed metric calculations support the robustness of the GP relation.

The relation is a universal feature of thermodynamics in power-law AdS black holes.

Abstract

This study investigates the universal relation between Goon and Penco (GP) proposed within the frameworks of Power-Maxwell, Power-Yang-Mills, and Maxwell-Power-Yang-Mills black holes. We begin by analyzing these black holes' thermodynamics and then calculating the perturbed metric and thermodynamic quantities by perturbing the action. Our objective is to examine the consistency of the GP relation across various power-law terms in the field equations, aiming to gain deeper insights into the nature of these black holes. The GP connection remains robust across different power spacetimes, indicating that this relation is a universal feature of black holes.