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 p q = ωρ q in which −1 < ω < − 1 3 . Our calculations are restricted to ansatz: ω = −1 ( the cosmological constant regime ) and ω = − 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.

We perform a phase space analysis of a non-minimally coupled modified gravity theory with the Lagrangian density of the form 1 2 f 1 (R) + [1 + λf 2 (R)]Lm, where f 1 (R) and f 2 (R) are arbitrary functions of the curvature scalar R and Lm is the matter Lagrangian density. We apply the dynamical system approach to this scenario in two particular models. In the first model we assume f 1 (R) = 2R with a general form for f 2 (R) and set favorable values for effective equation of state parameter which is related to the several epochs of the cosmic evolution and study the critical points and their stability in each cosmic eras. In the second case, we allow the f 1 (R) to be an arbitrary function of R and set f 2 (R) = 2R. We find the late time attractor solution for the model and show that this model has a late time accelerating epoch and an acceptable matter era.

In this paper we study the thermodynamics of Einstein-Gauss-Bonnet (EGB)-AdS black holes minimally coupled to a cloud of strings in an extended phase space where the cosmological constant is treated as pressure of the black holes and its conjugate variable is the thermodynamical volume of the black holes. To investigate the analogy between EGB black holes surrounded by a cloud of strings and liquidgas system we derive the analytical solutions of the critical points and probe the effects of a cloud of strings on P − V criticality. There is obtained resemblance between "small black hole/large black hole" (SBH/LBH) phase transition and the liquid-gas phase transition. We see that impact of a cloud of strings can bring Van der Waals-like behavior, in absence of the Gauss-Bonnet (GB) counterpart. In the other words, in the EGB black hole with α → 0 and when it is surrounded by a cloud of strings the Hawking-Page phase transition would be disappeared and SBH/LBH phase transition recovers. Also there is not happened Joule-Thomson effect. *

In this work we are about to investigate the effects of dark energy quintessence on the evolution of the computational complexity in the context of AdS/CFT correspondence. We use the conjecture "complexity = action" for a charged black hole surrounded by dark energy. Then we try to find how it affects on the complexity growth at the late time approximations under some conditions where the Lloyd bound satisfy in this new model. We also compare the late time approximation of action growth with perturbed geometry in small limits of shift function. Actually we investigate the evolution of complexity when thermofield double state on the boundaries is perturbed by local operator corresponding to a shock wave geometry as holographically. Furthermore we investigate the spread of this local shock wave in the presence of quintessence dark energy. *

We study effects of non-abelian gauge fields on the holographic characteristics for instance the evolution of computational complexity. To do so we choose Maxwell-power-Yang-Mills theory defined in the AdS space-time. Then we seek the impact of charge of the YM field on the complexity growth rate by using complexity = action (CA) conjecture. We also investigate the spreading of perturbations near the horizon and the complexity growth rate in local shock wave geometry in presence of the YM charge. At last we check validity regime of Lloyd bound. *