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

Abstract

In the extended phase space, we investigate the rainbow gravity-corrected thermodynamic phenomena and phase structure of a 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 restored the $P-V$ criticality and obtained 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-Nordstr\"{o}m anti-de Sitter black hole. Therefore, rainbow gravity activates the effect of electric charge and cutoff factor in the evolution of the black hole.

Absorption cross section in gravity’s rainbow from confluent Heun equation

“…proposed by Amelino-Camelia and Magueijo and Smolin, respectively. See [52][53][54] for recent works on the thermodynamics and phase transitions of rainbow black holes. We will consider generic rainbow functions to see the effect of gravity's rainbow on the absorption cross-section.…”

The Joule–Thomson and Joule–Thomson‐Like Effects of the Black Holes in a Cavity

“…The second choice of the extended phase space is to enclose the black hole in a cavity in asymptotically flat space, on the wall of which the metric is fixed (i.e., with the Dirichlet boundary condition). [ 7–42 ] In this way, the wall acts as a reflecting boundary against the Hawking radiation and thus stabilizes the black hole. Hence, the function of the cavity is similar to the AdS space, as the gravitational potentials increase at large distances in both of these two cases, only with different boundary conditions.…”