March 19, 2024 | Yahya Ladghami*, Brahim Asfour †1,2, Amine Bouali ‡1,2, Ahmed Errahmani §1,2, and Taoufik Ouali ¶1,2
This paper explores the impact of quantum gravity on the thermodynamics of charged AdS black holes using the restricted phase space (RPS) thermodynamics formalism. The authors investigate how quantum gravitational effects influence critical phenomena, phase transitions, and the stability of these black holes. They introduce a novel concept called "resistance of phase transitions," which refers to the delay or prevention of phase transitions due to the fractal structure of the event horizon area. The study reveals that the Smarr relation in RPS thermodynamics is violated due to the effects of quantum gravity, leading to a non-homogeneous property. The authors derive the thermodynamic variables and equations of state for charged AdS black holes with a fractal structure, and analyze the critical parameters and phase transitions. They find that as the fractal parameter increases, both critical entropy and phase transition entropies also increase, but at the maximum fractal level ($\delta=1$), critical quantities diverge, indicating the absence of phase transitions. The study concludes that the quantum gravitational effects on the event horizon area behave as a "resistance to phase transitions," delaying or preventing critical phenomena. The findings are similar to those observed in Van der Waals fluids, where the thermodynamic behavior is influenced by quantum gravity.This paper explores the impact of quantum gravity on the thermodynamics of charged AdS black holes using the restricted phase space (RPS) thermodynamics formalism. The authors investigate how quantum gravitational effects influence critical phenomena, phase transitions, and the stability of these black holes. They introduce a novel concept called "resistance of phase transitions," which refers to the delay or prevention of phase transitions due to the fractal structure of the event horizon area. The study reveals that the Smarr relation in RPS thermodynamics is violated due to the effects of quantum gravity, leading to a non-homogeneous property. The authors derive the thermodynamic variables and equations of state for charged AdS black holes with a fractal structure, and analyze the critical parameters and phase transitions. They find that as the fractal parameter increases, both critical entropy and phase transition entropies also increase, but at the maximum fractal level ($\delta=1$), critical quantities diverge, indicating the absence of phase transitions. The study concludes that the quantum gravitational effects on the event horizon area behave as a "resistance to phase transitions," delaying or preventing critical phenomena. The findings are similar to those observed in Van der Waals fluids, where the thermodynamic behavior is influenced by quantum gravity.