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 $r_h$ via a constant parameter $a$, we discuss the $P$-$v$ criticality behaviors by calculating the critical pressure $P_c$, the critical temperature $T_c$ and the critical specific volume $v_c$ in terms of $a$ and the rainbow gravity parameter $\epsilon$. As results, we reveal that the ratio ${\displaystyle \frac{P_c{v}_c}{T_c}}$ is an universal number with respect to the charge. In small limits of the external parameters, we recover the Van der Waals fluid behaviors.