Van der Waals criticality in AdS black holes: a phenomenological study

Abstract

AdS black holes exhibit van der Waals type phase transition. In the {\it 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 {\it 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.

arXiv commentRefs. and comments added, to appear in Phys. Rev. D

References in corpus (26)

• P-V criticality of charged AdS black holes
• Charged AdS Black Holes and Catastrophic Holography
• Black hole chemistry: thermodynamics with Lambda
• Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes
• P-V criticality in the extended phase space of Gauss-Bonnet black holes in AdS space
• Multiple Reentrant Phase Transitions and Triple Points in Lovelock Thermodynamics
• Thermodynamic Geometry and Critical Behavior of Black Holes
• Phase transition and Thermodynamical geometry of Reissner-Nordström-AdS Black Holes in Extended Phase Space
• P-V Criticality in Quasitopological Gravity
• Isolated critical point from Lovelock gravity
• Black holes in Einsteinian cubic gravity
• Reentrant phase transitions and van der Waals behaviour for hairy black holes
• P-V criticality of AdS black holes in a general framework
• Van der Waals phase transition in the framework of holography
• Phase transition of holographic entanglement entropy in massive gravity
• P-V criticality of first-order entropy corrected AdS black holes in massive gravity
• Thermodynamics of hairy black holes in Lovelock gravity
• Thermogeometric description of the van der Waals like phase transition in AdS black holes
• Geometrical thermodynamics and P-V criticality of the black holes with power-law Maxwell field
• Thermogeometric phase transition in a unified framework
• Phase transition and critical phenomena of black holes: A general approach
• Thermal phase transitions of dimensionally continued AdS black holes
• $Q-\Phi$ criticality in the extended phase space of $(n+1)$-dimensional RN-AdS black holes
• Maxwell's equal area law for black holes in power Maxwell invariant
• A consistent and unified picture for critical phenomena of $f(R)$ AdS black holes
• Black hole free energy during charged collapse: a numerical study

Cited by in corpus (46)

• Effects of energy dependent spacetime on geometrical thermodynamics and heat engine of black holes: gravity's rainbow
• Thermal Dynamic Phase Transition of Reissner-Nordström Anti-de Sitter Black Holes on Free Energy Landscape
• Microstructure and continuous phase transition of RN-AdS black hole
• Dynamic properties of thermodynamic phase transition for five-dimensional neutral Gauss-Bonnet AdS black hole on free energy landscape
• Holographic Entanglement Entropy in the QCD Phase Diagram with a Critical Point
• Continuous phase transition and microstructure of charged AdS black hole with quintessence
• Phase Structures and Transitions of Born-Infeld Black Holes in a Grand Canonical Ensemble
• A general framework to study the extremal phase transition of black holes
• Topological interpretation of extremal and Davies-type phase transitions of black holes
• P-V criticality in the extended phase space of black holes in Einstein-Horndeski gravity
• Fokker-Planck equation for black holes in thermal potential
• Universality class of alternative phase space and Van der Waals criticality
• Black hole evaporation in Conformal (Weyl) gravity
• $P-v$ criticality of a specific black hole in $f(R)$ gravity coupled with Yang-Mills field
• Thermogeometric study of van der Waals like phase transition in black holes: an alternative approach
• Thermodynamics and weak cosmic censorship conjecture in the Kerr-AdS black hole
• Rate of the phase transition for a charged anti-de Sitter black hole
• Photon orbits and phase transition for Non-Linear charged Anti-de Sitter black holes
• van der Waals fluid and charged AdS black hole in the Landau theory
• Phase Transition Dynamics of Black Holes Influenced by Kaniadakis and Barrow Statistics
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
• First Principle Study of Gravitational Pressure and Thermodynamics of FRW Universe
• Divergence Behavior of Thermodynamic Curvature Scalar at Critical Point in the Extended Phase Space of Generic Black Holes
• Shadow thermodynamics of non-linear charged Anti-de Sitter black holes
• The Hawking-Page-like Phase Transition from FRW Spacetime to McVittie Black Hole
• Thermodynamics and weak cosmic censorship conjecture of an AdS black hole with a monopole in the extended phase space
• Dynamic Property of Phase Transition for Non-Linear Charged Anti-de Sitter black holes
• Topology and phase transition for EPYM AdS black hole in thermal potential
• Insight into the Microstructure of FRW Universe from a $P$-$V$ Phase Transition
• Topology of the charged AdS black hole in restricted phase space
• Microstructure and Continuous Phase Transition of the Gauss-Bonnet AdS Black Hole
• Thermodynamic phase transition and winding number for the third-order Lovelock black hole
• Quasinormal Modes and Van der Waals like phase transition of charged AdS black holes in Lorentz symmetry breaking massive gravity
• Continuous Phase Transition of the higher-dimensional topological de-Sitter Spacetime with the Non-linear Source
• Revisiting thermodynamic topology of Hawking-Page and Davies type phase transitions
• Static spherically symmetric black hole's solution in Einstein-Maxwell-Yang-Mills-dilaton theory
• Overview of thermodynamic properties for Reissner-Nordstrom-de Sitter spacetime in induced phase space
• On the thermodynamic phase structure of conformal gravity
• Fractional-order phase transition of charged AdS black holes
• Structure and thermodynamics of charged nonrotating black holes in higher dimensions
• Hawking-Page Phase Transition of the four-dimensional de-Sitter Spacetime with non-linear source
• Dark Energy Accretion onto Van der Waal's Black Hole
• Quantum State Dependence of Thermodynamic Phase Transition in 4D AdS Gauss-Bonnet Quantum Black Holes Surrounded With Cloud of Strings
• Thermodynamic and observational implications of black holes in toroidal geometry
• RPST-Inspired Formalism for Black Holes in Flat Spacetime
• Some perspective of thermodynamical and optical properties of black holes in Maxwell-dilaton-dRGT-like massive gravity