Van der Waals-like behaviour of charged black holes and hysteresis in the dual QFTs

Abstract

Using the rules of the AdS/CFT correspondence, we compute the spherical analogue of the shear viscosity, defined in terms of the retarded Green function for the stress-energy tensor for QFTs dual to five-dimensional charged black holes of general relativity with a negative cosmological constant. We show that the ratio between this quantity and the entropy density, η˜/s, exhibits a temperature-dependent hysteresis. We argue that this hysteretic behaviour can be explained by the Van der Waals-like character of charged black holes, considered as thermodynamical systems. Under the critical charge, hysteresis emerges owing to the presence of two stable states (small and large black holes) connected by a meta-stable region (intermediate black holes). A potential barrier prevents the equilibrium path between the two stable states; the system evolution must occur through the meta-stable region, and a path-dependence of η˜/s is generated

Hysteresis in $$\eta /s$$ η / s for QFTs dual to spherical black holes

“…In this section we extend the discussion of Ref. [45]. For neutral AdS BHsη/s starts at the universal value 1/4π at large temperatures and decreases monotonically as T decreases, reaching a minimum non-zero value for the non-vanishing minimum temperature T = √ 2/π .…”

“…In fact, the BH temperature serves as a function of the radius, Eq. (20), when Q = 0 becomes a monotonic function and shows no Van der Waals-like behavior as in the RN case [45].…”

“…In a recent letter [45], a definition of the shear viscosity for QFTs living in manifolds whose spatial sections are spheres is proposed. This has allowed us to compute the spherical analog of the shear viscosityη for QFTs dual to five-dimensional AdS-Reissner-Nordström (AdS-RN) BHs in GR.…”

Van der Waals-Like Phase Transition from Holographic Entanglement Entropy in Lorentz Breaking Massive Gravity

“…Very recently, the equal area law of HEE was proved to hold for the FPT in the HEE-temperature plane [22]. Based on [20], VDP phase transition of HEE in various AdS black holes have been studied in [23,24,25,26,27,28,29,30,31,32]. All of these works showed that the HEE undergoes the same VDP phase transition as that of the BHE.…”

Dark Energy Accretion onto Van der Waal’s Black Hole

“…For a small scale connected to the inverse cosmological constant Λ, l is a parameter with dimensions of length (Hubble length) and the parameter a vw > 0 measures the attraction between the molecules of the fluid, and the parameter b vw measures their volume. We find several literatures, nowadays, where [13,14] the thermodynamic natures of the Van der Waal's black holes have been studied. A common conclusion drawn from all these articles is that the Van der Waal's black hole solution is qualitatively analogical (on a thermodynamic perspective) with the Van der Waal's fluid.…”