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–Nordstr?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.

Temporal and spatial chaos in the Kerr-AdS black hole in an extended phase space

Based on the Melnikov method,we investigate chaotic behaviors in the extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole under temporal and spatial perturbations.Our results show that the temporal perturbation coming from a thermal quench of the spinodal region in the phase diagram may cause temporal chaos only when the perturbation amplitude is above a critical value,which involves the angular momentum J.Under the spatial perturbation,however,it is found that spatial chaos always occurs,independent of the perturbation amplitude.

Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter

We obtain an exact solution for spherically symmetric Letelier AdS black holes immersed in perfect fluid dark matter(PFDM).Considering the cosmological constant as the positive pressure of the system and volume as its conjugate variable,we analyze the thermodynamics of our black holes in the extended phase space.Owing to the background clouds of strings parameter(a)and the parameter endowed with PFDM(β),we analyze the Hawking temperature,entropy,and specific heat.Furthermore,we investigate the relationship between the photon sphere radius and phase transition for the Letelier AdS black holes immersed in PFDM.Through the analysis,with a particular condition,non-monotonic behaviors are found between the photon sphere radius,impact parameter,PFDM parameter,temperature,and pressure.We can regard the changes in both the photon sphere radius and impact parameter before and after phase transition as the order parameter;their critical exponents near the critical point are equal to the same value,1/2,similar to that in ordinary thermal systems.This indicates that a universal relation of gravity may exist near the critical point for a black hole thermodynamic system.

Thermodynamics and weak cosmic censorship conjecture of charged AdS black hole in the Rastall gravity with pressure

Treating the cosmological constant as a dynamical variable,we investigate the thermodynamics and weak cosmic censorship conjecture(WCCC)of a charged AdS black hole(BH)in the Rastall gravity.We determine the energy momentum relation of charged fermion at the horizon of the BH using the Dirac equation.Based on this relation,it is shown that the first law of thermodynamics still holds as a fermion is absorbed by the BH.However,the entropy of both the extremal and near-extremal BH decreases in the irreversible process,which means that the second law of thermodynamics is violated.Furthermore,we verify the validity of the WCCC by the minimum values of the metric function h(r)at its final state.For the extremal charged AdS BH in the Rastall gravity,we find that the WCCC is always valid since the BH is extreme.While for the case of near-extremal BH,we find that the WCCC could be violable in the extended phase space(EPS),depending on the value of the parameters of the BH and their variations.

Hawking-Page phase transitions of charged AdS black holes surrounded by quintessence

Hawking-Page phase transitions between the thermal anti-de Sitter vacuum and charged black holes surrounded by quintessence are studied in the extended phase space.The quintessence field,with the state parameter-1<w<-1/3,modifies the temperature and the Gibbs free energy of a black hole.The phase transition temperature Thp and the Gibbs free energy G are first analytically investigated for the special case of w=-2/3,and then,the results of numerical simulations are shown for general w.The phase transition temperature Thp increases with pressure and decreases with electric potential.In addition,Thp significantly decreases owing to the quintessence field,which generates negative pressure around the black hole.