Quantum corrections to the thermodynamics and phase transition of a black hole surrounded by a cavity in the extended phase space

In the extended phase space, we investigate the rainbow gravity-corrected thermodynamic phenomena and phase structure of the Schwarzschild black hole surrounded by a spherical cavity. The results show that rainbow gravity has a very significant effect on the thermodynamic phenomena and phase structure of the black hole. It prevents the black hole from total evaporation and leads to a remnant with a limited temperature but no mass. Additionally, we restore the P - V criticality and obtain the critical quantities of the canonical ensemble. When the temperature or pressure is smaller than the critical quantities, the system undergoes two Hawking-Page-like phase transitions and one first-order phase transition, which never occurs in the original case. Remarkably, our findings demonstrate that the thermodynamic behavior and phase transition of the rainbow SC black hole surrounded by a cavity in the extended phase space are analogous to those of the Reissner-Nordstrom anti-de Sitter black hole. Therefore, rainbow gravity activates the effect of electric charge and cutoff factor in the evolution of the black hole.

Automated summary

In this study, we investigate the rainbow gravity-corrected thermodynamic phenomena and phase structure of the Schwarzschild black hole surrounded by a spherical cavity in the extended phase space. The results show that rainbow gravity has a significant effect on the thermodynamic phenomena and phase structure of the black hole, preventing total evaporation and leading to a remnant with limited temperature but no mass. Additionally, we restore the criticality of the P-V ensemble and observe two Hawking-Page-like phase transitions and one first-order phase transition, which are not present in the original case. Importantly, our findings demonstrate that the thermodynamic behavior and phase transition of the rainbow SC black hole surrounded by a cavity in the extended phase space are similar to those of the Reissner-Nordstrom anti-de Sitter black hole, indicating the activation of electric charge and cutoff factor in the evolution of the black hole.