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

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.

💡 Research Summary

The paper investigates the thermodynamic properties of Reissner‑Nordström‑Anti‑de Sitter (RN‑AdS) black holes that are immersed in a perfect fluid dark matter (PFDM) background. The analysis is performed in two complementary frameworks: the restricted phase space thermodynamics (RPS) and the conformal field theory (CFT) side of the AdS/CFT correspondence. A central focus is the Goon‑Penco (GP) relation, which links variations of the extremal mass with variations of the entropy and temperature under a perturbative parameter η that encodes higher‑order corrections (e.g., higher‑derivative terms). The GP relation reads

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