Universal relations with the non-extensive entropy in the RPS and CFT framework

TL;DR

This work tests the universality of the Goon-Penco relation, linking entropy corrections to extremality, for RN-AdS black holes surrounded by PFDM in both restricted phase space thermodynamics (RPST) and CFT holographic frameworks. It shows that the GP relation holds not only with the Bekenstein-Hawking entropy but also when the entropy is generalized to non-extensive Barrow, Renyi, and Sharma-Mittal forms. The results demonstrate a robust, framework- and entropy-form independent connection between mass/energy corrections and entropy variations, anchored to the first law of thermodynamics. This strengthens the GP relation as a universal thermodynamic principle in black hole physics and aids connections to quantum gravity concepts like the WGC.

Abstract

In this paper, an in-depth investigation of the thermodynamic relations for AdS Reissner-Nordstr$\ddot{o}$m black holes immersed in perfect fluid dark matter (PFDM) is presented. This investigation is conducted within both the restricted phase space (RPS) and the conformal field theory (CFT) frameworks. The influence of non-extensive forms of entropy is also systematically examined. Our results demonstrate that the Goon-Penco (GP) relation for charged AdS black holes holds within both the RPS and CFT frameworks, irrespective of the specific form of entropy modification. The conclusion of the present study demonstrates that the GP relation constitutes a universal thermodynamic relation.