Q– $$\Phi $$ Φ criticality in the extended phase space of $$(n+1)$$ ( n + 1 ) -dimensional RN-AdS black holes

Abstract

In order to achieve a deeper understanding of gravity theories, i.e., the quantum properties of gravity theories and the statistical explanation of gravitational entropy, it is important to further investigate the thermodynamic properties of a black hole at the critical point, besides the phase transition and critical behaviors. In this paper, by using Maxwell's equal area law, we choose T, Q, as the state parameters and study the phase equilibrium problem of a general (n + 1)-dimensional RN-AdS black holes thermodynamic system. The boundary of the two-phase coexistence region and its isotherm and isopotential lines are presented, which may provide a theoretical foundation for studying the phase transition and phase structure of black hole systems.

Universal ratios of critical physical quantities of charged AdS black holes

“…Ref. [26] studied Q − Φ criticality of (n + 1)-dimensional (Note that n = d − 1.) charged AdS black hole.…”

“…On the other hand, Ref. [26] recently investigated the Q − Φ criticality of d-dimensional charged black holes and argued that the ratio ΦcQc Tc is not universal. To explain this phenomenon, we will also carry out some discussion on the universal ratios for P − V criticality and Q − Φ criticality in this paper.…”

Thermogeometric study of van der Waals like phase transition in black holes: An alternative approach

“…The van der Waals type criticality has also been obtained for the charge-potential [27] and also for angular momentum-angular velocity in the non extended phase space. We generally call it as the Y − X criticality as, in our case, Y i represents all the charges, angular momentum etc.…”

“…As shown in the Figure 1 of [27], in this case the criticality relation is obtained between a particular charge Y and its potential X while all other charges and potentials are kept fixed. Then in Y − X plane we draw the isothermal lines and shows that on the critical isotherm the critical point is located at the point where the criticality conditions are satisfied.…”

“…In the AdS space, when the cosmological constant is regarded as the thermodynamic pressure [13][14][15][16][17], it was found that the P − V diagram of black holes in the extended phase space looks exactly similar to that of the ordinary thermodynamics [18,19], which implies a van der Waals phase transition in the black hole thermodynamics. Apart from the P − V criticality, there are also a few other criticalities in black hole space which also are of van der Waals type, like T − S criticality [20][21][22][23][24][25][26], Q − Φ criticality [27], Q 2 − Ψ criticality [28,29] etc. In addition, the van der Waals type phase transition has also been observed in [30], where the phase transition of black holes has been studied in AdS 5 × S 5 spacetime by considering the cosmological constant as the number of colors in the boundary gauge theory and its conjugate quantity as corresponding chemical potential.…”