P-V criticality in the extended phase-space of charged accelerating AdS black holes

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 A 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 rh meet a certain simple relation Ar-h = alpha, where a is a constant in our discussion. To make P-V criticality appear, there exists an upper bounds for constant alpha. 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 P(c)r(c)/T-c is an universal number.