Critical behavior of charged AdS black holes surrounded by quintessence via an alternative phase space

Abstract

Variation of the pressure of the bulk, or equivalently variation of the AdS radius (l) leads to variation of the boundary quantities: i) the number of colors N . ii) the volume of the space on which the field theory is formulated (since V ∝ l d−2 ). iii) the CFT charge Q which is related to the bulk charge Q b according to Q = lQ b . So, considering the cosmological constant as a new thermodynamical parameter may give the phase diagram an extra dimension. An alternative interpretation is suggested in [12], where the variation of the pressure in the bulk theory corresponds to vary the volume of the boundary field theory. In this approach, the number of colors is kept fixed, which requires the variation of Newton's constant to compensate the variation of the volume of the boundary field theory. This shows that one cannot employ such an approach (AdS/CFT correspondence) to investigate the extended thermodynamics of black holes.Considering the defined thermodynamic pressure and volume, one can study thermodynamics of black holes in a new framework, sometimes referred to as Black Hole Chemistry [13]. This change of perspective has led to a different concept of known processes and the discovery of a broad range of new phenomena associated with black holes such as van der Waals behavior [9,14], solid/liquid phase transitions [15], triple points [16], reentrant phase transitions [17] and heat engines [11]. Also, using black hole volume, one can study the black hole adiabatic compressibility which has attracted attention in connection with black hole stability [18]. This new perspective has also been successful in describing the thermodynamic structure of black holes in other gravitational theories such as Lovelock gravity [19], nonlinear electrodynamics [20], Einstein-Yang-Mills gravity [21], black holes with scalar hair [22], dyonic black holes [23], f(R) gravity [24], STU black holes [25], quasi topological gravity [26], conformal gravity [27] Poincare gauge gravity [28], Lifshitz gravity [29-31] and massive gravity [32].Since the thermodynamic behavior of black hole is highly affected by the variation of electric charge, an alternative approach for investigating van der Waals like phase transition is proposed [33,34] by considering the electric charge as a thermodynamic variable and fixing the cosmological constant. In this regard, a phase transition between the large and small black holes in the Q − Φ plane is seen. In addition, it is shown that [35] such a suggestion is mathematically problematic and physically unconventional and it is logical to consider the square of the electric charge, Q 2 , as a thermodynamic variable. In Ref. [35], the van der Waals like behavior of charged AdS black hole in Q 2 − Ψ plane with a fixed cosmological constant is studied. It is also obtained the critical exponents which were exactly coincident with those obtained for van der Waals liquid. As a keynote, we should emphasize that unlike the van der Waals liquid the mentioned phase transition occurred for temperature higher than criti...

Can we know about black hole thermodynamics through shadows?

“…Now black hole is not only regarded as a strong gravitational system, but also as a thermodynamic one, so it is necessary to explore the relationship between its dynamics and thermodynamics. Recently, the relationships between dynamic characteristic quantities and thermodynamic ones have been studied [65][66][67][68][69][70][71][72][73][74]. Some results show [65,66] that the unstable circular orbital motion can connect thermodynamic phase transitions of black holes.…”

Phase structures and transitions of quintessence surrounding RN black holes in a grand canonical ensemble *

“…Since then, a series of studies about black holes in the presence of quintessence have been conducted. Quintessence modes were studied in [55,56], and thermodynamics including Hawking radiation, heat engines, and phase transition in the holographic framework were investigated in [57][58][59][60][61][62][63][64][65][66]. In particular, the phase transition of the quintessence RN-dS black hole was studied through the effective thermodynamic quantities [67].…”

Phase Structures and Transitions of Quintessence Surrounding RN Black Holes in a Grand Canonical Ensemble

“…Quintessence modes were studied in [55,56], thermodynamics including Hawking radiation, heat engine, phase transition in the holographic framework and so on were investigated in [57][58][59][60][61][62][63][64][65][66]. Especially, the phase transition of the quintessence RN-dS black hole was studied through the effective thermodynamic quantities [67].…”