Quintessence Reissner Nordström Anti de Sitter Black Holes and Joule Thomson effect

Abstract: In this work we investigate corrections of the quintessence regime of the dark energy on the Joule-Thomson (JT) effect of the Reissner Nordstr\"om anti de Sitter (RNAdS) black hole. The quintessence dark energy has equation of state as $p_q=\omega\rho_q$ in which $-1<\omega<-\frac{1}{3}.$ Our calculations are restricted to ansatz: $\omega=-1$ (the cosmological constant regime) and $\omega=-\frac{2}{3}$ (quintessence dark energy). To study the JT expansion of the AdS gas under the constant black hole mass, we calculate inversion temperature $T_i$ of the quintessence RNAdS black hole where its cooling phase is changed to heating phase at a particular (inverse) pressure $P_i.$ Position of the inverse point ${T_i,P_i}$ is determined by crossing the inverse curves with the corresponding Gibbons-Hawking temperature on the T-P plan. We determine position of the inverse point verse different numerical values of the mass $M$ and the charge $Q$ of the quintessence AdS RN black hole. The cooling-heating phase transition (JT effect) is happened for $M>Q$ in which the causal singularity is still covered by the horizon. Our calculations show sensitivity of the inverse point ${T_i,P_i}$ position on the T-P plan to existence of the quintessence dark energy just for large numerical values of the AdS RN black holes charge $Q$. In other words the quintessence dark energy dose not affects on position of the inverse point when the AdS RN black hole takes on small charges.