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.

Using some suitable combinations of a dynamical unit time-like fourvelocity of a preferred reference frame, Ricci tensor and covariant derivatives of the Brans-Dicke (BD) scalar field, we propose a new scalar-vector-tensor gravity model in which an Euclidean Jordan-Brans-Dicke (JBD) action is reduced to its Lorentzian version with no used complex coordinates. Thus it should be play an important role in the process of metric signature transition of a suitable dynamical curved spacetime. In this work we follow the ideas proposed by Barbero et al. As an application of the model, we study a classical perfect fluid cosmological universe described in a flat Robertson-Walker background metric. Mathematical derivations of the equations predict a non-singular scale factor for the space-time in the both of dust and radiation dominated states where value of the Brans-Dicke parameter ω is fixed, but there is still an arbitrary parameter which should be determined by the boundary values of the cosmological system. Furthermore its classical cosmological vacuum solutions is obtained as a non-singular model with a fixed Brans-Dicke parameter. Although there is obtained a singular perfect fluid cosmological solution which may not be suitable, because in this case the Brans-Dicke parameter is not still fixed.

In this article we study weak gravitational lensing of regular Bardeen black hole which has scalar charge g and mass m. We investigate the angular position and magnification of non-relativistic images in two cases depending on the presence or absence of photon sphere. Defining dimensionless charge parameter q = g 2m we seek to disappear photon sphere in the case of |q| > 24 √ 5/125 for which the space time metric encounters strongly with naked singularities. We specify the basic parameters of lensing in terms of scalar charge by using the perturbative method and found that the parity of images is different in two cases: (a) The strongly naked singularities is present in the space time. (b) singularity of space time is weak or is eliminated (the black hole lens).

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. *

The relation (3.3) should be corrected with ξ = 1. In that case the action functional defined by (3.5) becomesCorrected forms of the equations defined by (3.6) and (3.7) will be, respectively,The online version of the original article can be found under