Stability and Criticality Behaviors of Accelerating Charged AdS Black Holes in Rainbow Gravity

In this work, we investigate the thermodynamical properties of accelerated charged Anti-de Sitter black holes in the context of rainbow gravity. Concretely, we compute the corresponding quantities needed to study the thermal stability and the critical behaviors including the phase transitions. Linking the acceleration parameter A and the horizon radius rₕ via a constant parameter a, we discuss the P-v criticality behaviors by calculating the critical pressure Pc, the critical temperature Tc and the critical specific volume vc in terms of a and the rainbow gravity parameter ε. As results, we reveal that the ratio PcvcTc is an universal number with respect to the charge. In small limits of the external parameters, we recover the Van der Waals fluid behaviors.