Quintessence Reissner Nordström Anti de Sitter Black Holes and Joule Thomson Effect.

In this work we investigate corrections of the quintessence regime of the dark energy on the Joule-Thomson (JT) effect of the Reissner Nordström anti de Sitter (RNAdS) black hole. The quintessence dark energy has equation of state as <italic>p</italic><italic>q</italic> = <italic>ω</italic><italic>ρ</italic><italic>q</italic> in which −1<ω<−13<inline-graphic></inline-graphic>. Our calculations are restricted to ansatz: <italic>ω</italic> = − 1 (the cosmological constant regime) and ω=−23<inline-graphic></inline-graphic> (quintessence dark energy). To study the JT expansion of the AdS gas under the constant black hole mass, we calculate inversion temperature <italic>T</italic><italic>i</italic> of the quintessence RNAdS black hole where its cooling phase is changed to heating phase at a particular (inverse) pressure <italic>P</italic><italic>i</italic>. Position of the inverse point {<italic>T</italic><italic>i</italic>, <italic>P</italic><italic>i</italic>} 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 versus different numerical values of the mass <italic>M</italic> and the charge <italic>Q</italic> of the quintessence AdS RN black hole. The cooling-heating phase transition (JT effect) is happened for <italic>M</italic> > <italic>Q</italic> in which the causal singularity is still covered by the horizon. Our calculations show sensitivity of the inverse point {<italic>T</italic><italic>i</italic>, <italic>P</italic><italic>i</italic>} 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 <italic>Q</italic>. In other words the quintessence dark energy dose not affect on position of the inverse point when the AdS RN black hole takes on small charges. [ABSTRACT FROM AUTHOR]