$P-V$ Criticality In the Extended Phase Space of Charged Accelerating AdS Black Holes

Abstract

In this paper, we investigate the $P-V$ criticality and phase transition of charged accelerating AdS black holes in the extended thermodynamic phase space in analogy between black hole system and Van der Waals liquid-gas system, where the cosmological constant $\hat{I}›$ is treated as a thermodynamical variable interpreted as dynamic pressure and its conjugate quantity is the thermodynamic volume of the black holes. When the electric charge vanishes, we find that no $P-V$ criticality will appear but the Hawking-Page like phase transition will be present, just as what Schwarzschild-AdS black holes behave like. For the charged case, the $P-V$ criticality appears and the accelerating black holes will undergo a small black hole/large phase transition under the condition that the acceleration parameter $A$ and the horizon radius $r_h$ meet a certain simple relation $A{r}_h=a$, where $a$ is a constant in our discussion. To make $P-V$ criticality appear, there exists an upper bounds for constant $a$. When $P-V$ criticality appears, we calculate the critical pressure $P_c$, critical temperature $T_c$ and critical specific volume $r_c$, and we find that $\frac{P_c{r}_c}{T_c}$ is an universal number.

14pages,5 figures,references added