van der Waals criticality in AdS black holes: A phenomenological study

Abstract

AdS black holes exhibit van der Waals type phase transition. In the extended phase-space formalism, the critical exponents for any spacetime metric are identical to the standard ones. Motivated by this fact, we give a general expression for the Helmholtz free energy near the critical point which correctly reproduces these exponents. The idea is similar to the Landau model which gives a phenomenological description of the usual second order phase transition. Here two main inputs are taken into account for the analysis: (a) black holes should have van der Waals like isotherms and (b) free energy can be expressed solely as a function of thermodynamic volume and horizon temperature. Resulting analysis shows that the form of Helmholtz free energy correctly encapsulates the features of Landau function. We also discuss the isolated critical point accompanied by nonstandard values of critical exponents. The whole formalism is then extended to other two criticalities, namely Y − X and T − S (based on the standard; i.e. non-extended phase-space), where X and Y are generalized force and displacement, whereas T and S are horizon temperature and entropy. We observe that in the former case Gibbs free energy plays the role of Landau function, whereas in the later case that role is played by the internal energy (here it is black hole mass). Our analysis shows that, although the existence of van der Waals phase transition depends on the explicit form of the black hole metric, the values of the critical exponents are universal in nature.

Universality class of alternative phase space and Van der Waals criticality

“…It was indeed shown that in this alternative phase space, phase transition and critical behavior of RN-AdS black hole, in four dimensions, occur in the Q 2 -Ψ plane, where relevant response function clearly signifies stable and unstable region [1]. Remarkably, in this viewpoint, the small-large black hole phase transition is quite similar to the Van der Waals liquid-gas system and belongs to the same universality class in contrast with previous study of [16]. Additionally, it would be interesting to study the universality class and critical properties for any AdS black hole in an alternative phase space where the cosmological constant (Λ) is taken to be constant.…”

“…In this view, the thermodynamic behavior of AdS black hole is analyzed in a thermodynamics phase space. The critical point and associated critical exponents in a phase space of black hole have been studied in a general way [16]. It was found that the values of critical exponents differ from those of the Van der Waals phase transition [16].…”

“…The critical point and associated critical exponents in a phase space of black hole have been studied in a general way [16]. It was found that the values of critical exponents differ from those of the Van der Waals phase transition [16]. All these phase transitions are also discussed from the thermogemetrical point of view [17] where the phase transition is identified as the divergence of the Ricci scalar of the thermodynamic geometry.…”

General framework to study the extremal phase transition of black holes

“…For non-extremal black holes, there are two major approaches of studying the phase transition of black hole-one approach deals with the divergence of heat capacity and inverse of isothermal compressibility [31][32][33][34][35][36][37][38]. The other approach [39][40][41][42] is for the black holes in the AdS background, in which the cosmological constant is treated as the thermodynamic pressure. The latter approach exactly resembles the phase transition of the van der Waals fluid system.…”

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

“…Although the analysis apparently is intriguing, its main limitation was the lack of a proper canonical definition of P and V variables. Later on, when the cosmological constant was taken as a variable and included in the extended version of first law [13][14][15][16][17] (also see our work [65], where the first law in the extended phase space has been obtained from the conserved Noether current following Wald's method), the canonical definition of P and V was provided and was shown that the van der Waals P − V criticality exists in black hole spacetime [18,19,74,75] and at the critical point, two independent conditions coincide i.e.…”