P-V Criticality And Holographic Heater Efficiency Of AdS Black Holes In DRGT Mass Gravity

In this paper,the P-V criticality and holographic heat engine are studied from the AdS black hole in dRGT(de Rham-Gabadadze-Tolley)mass gravity.The influence of different parameters on criticality and engine efficiency is also discussed.Firstly,the P-V criticality is studied from the AdS black hole in dRGT mass gravity.Thermodynamic quantities are calculated,such as specific heat capacity,critical pressure and critical temperature.P-v images with different values of parameter??,?,c are ploted,and it is found,when T?T_C there is a first-order phase transition similar to Van der Waals gas-liquid phase transition,there is a second-order phase transition occurs when T=T_C and no phase transition when T?T_C.Hawking-Page-like phase transition can be observed when the black hole is uncharged.In order to verify the stability of black holes,we plot C_P-S images and G-P images,and studies in detail the local stability and global stability of black hole thermodynamics.And the influence of various parameters on the stability can be discussed.The results show that whenP?P_C,the black hole is locally stable.When P?P_C,the small black hole is locally stable,the middle black hole is locally unstable and the big black hole is locally stable.Therefore black hole has experienced the first-order phase transition from small black holes to large black holes.When P=P_C,the heat capacity has a singular point at the critical value S_C,so the black hole has undergone a second-order phase transition.WhenP?P_C,the black hole is locally stable.It can be seen that the AdS black hole with dRGT mass gravitation has van der Waals phase transition which is similar to the phase transition between gas and liquid at constant temperature.When studying the global stability,whenT?T_C,there is a dovetail shape in the image,and there is a first-order phase transition between the small black hole and the big black hole.When the temperature rises to the critical value T_C,the dovetail shape disappears.Under high pressure,the big black hole is more stable.Secondly,we discusses the holographic heat engine of AdS black hole with dRGT mass gravity.The efficiencies of holographic heat engine with AdS black hole of dRGT mass gravity as working medium under Carnot cycle and rectangular cycle are calculated respectively.It is found that the efficiency of Carnot cycle is determined by the temperature of high and low temperature heat sources,and the rectangular cycle efficiency of this heat engine is consistent with the efficiency formula proposed by Clifford V.Johnson.The efficiency of Carnot cycle increases monotonously with the increase of parameters??and??,and increases first and then decreases with the increase of parameter c.With the increase of parameters??and??,the efficiency of rectangular cycle of heat engine decreases,and with the increase of parameter c,the efficiency of rectangular cycle first decreases and then increases.Therefore,the parameters related to gravitational mass have an important influence on the heat engine efficiency of AdS black holes in dRGT mass gravity...