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

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.