P-V criticality and Joule-Thomson expansion of charged AdS black holes in the Rastall gravity *

Abstract

We discuss the criticality and the Joule-Thomson expansion of charged AdS black holes in the Rastall gravity. We find that although the equation-of-state of a charged AdS black hole in the Rastall gravity is related to the Rastall parameter , its reduced equation-of-state at the critical point is independent of the Rastall parameter , as is the case in the Einstein gravity where . This is the reason why the critical exponents are not related to the Rastall parameter . We also find that the inversion temperature is related to the Rastall parameter , but that the minimum inversion temperature and the ratio between the minimum inversion temperature and the critical temperature are both independent of the Rastall parameter . At the critical point, the thermodynamic evolution of a charged AdS black hole in the Rastall gravity behaves as in the van der Waals fluid and charged AdS black hole in the Einstein gravity. We show the inversion curves and isenthalpic curves in the plane and analyze the effect of the Rastall constant on the inversion curves of a charged AdS black hole during the Joule-Thomson expansion.

Joule‐Thomson Expansion and Optical Behaviour of Reissner‐Nordström‐Anti‐de Sitter Black Holes in Rastall Gravity Surrounded by a Quintessence Field

“…we calculate the Joule‐Thomson coefficient μ of the black hole in order to determine its heating and cooling phases when dealing with the isenthalpic expansion. To obtain an expression of the Joule‐Thomson expansion coefficient, we start with the specific heat at a constant pressure of the black hole, which can be obtained from the first law of thermodynamics as given by [ 20 ] $$$$\begin{equation} C_p = T {\left(\frac{\partial S}{\partial T} \right)}_{P,Q,\beta }. \end{equation}$$$$In this case, the isobaric heat capacity takes the following form: $$$$\begin{equation} C_p = \frac{2 \pi (\beta -1) {\left[(\beta -1) r_h^{\frac{3 \beta }{\beta -1}} A_1- r_h^3 A_2\right]}}{r_h {\left[(\beta -1)^2 r_h^{\frac{3}{\beta -1}} {\left(A_1+4 Q^2\right)}+3 \beta A_2\right]}}, \end{equation}$$$$where $$A_1 = 8 \pi P r_h^4-r_h^2-Q^2$$ and $$A_2 = (\beta +2) N_s$$.…”

“…As a result, we use this analogous idea to understand black hole thermodynamics, and for that, we keep the black hole's enthalpy M constant or fixed. The Joule‐Thomson coefficient μ is given by, [ 19,20 ] $$$$\begin{equation} \mu = {\left(\frac{\partial T_H}{\partial P} \right)}_M = \frac{1}{C_p} {\left[ T_H {\left(\frac{\partial V}{\partial T}\right)}_P -V \right]}. \end{equation}$$$$During the expansion of a black hole, pressure always decreases, resulting in the change in pressure always being negative.…”

“…In a recent study, $$P-V$$ criticality and Joule‐Thomson expansion of charged anti‐de Sitter black holes in Rastall gravity have been extensively studied. [ 20 ] In this study, the inversion curves and isenthalpic curves in the $$T-P$$ plane have been investigated, and the impacts of the Rastall parameter have been studied. However, in this study, there was no additional surrounding field apart from the cosmological constant.…”

$P-V$ criticality and Joule-Thomson Expansion of Hayward-AdS black holes in 4D Einstein-Gauss-Bonnet gravity

“…The inversion and isenthalpic curves were obtained and the heating-cooling regions were illustrated in the T −P plane. Subsequently, Joule-Thomson expansions in various black holes have been studied extensively, such as 4D Gauss-Bonnet AdS black hole [35], Born-Infeld AdS black hole [36], charged AdS black hole in massive gravity [37], Lovelock AdS black hole [38], 5D Einstein-Maxwell-Gauss-Bonnet-AdS black hole [39], hyperscaling violating black hole [40], charged AdS black holes in the Rastall gravity [41],…”

Joule-Thomson expansion of Lower-dimensional black hole

“…Kerr-AdS black holes [47], regular(Bardeen)-AdS black holes [48], RN-AdS black holes in f (R) gravity [49], quintessence RN-AdS black holes [50], Bardeen-AdS black holes [51] and other black holes [52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71]. In these papers, the inversion curves, the isenthalpic curves and the heating-cooling regions in the T −P plane for different black holes were given.…”