Thermogeometric description of the van der Waals like phase transition in AdS black holes

Abstract

It is well known that interpreting the cosmological constant as the pressure, the AdS black holes behave as the van der Waals thermodynamic system. In this case, like a phase transition from vapor to liquid in a usual van der Waals system, black holes also changes phases about a critical point in the $P$-$V$ picture, where $P$ is the pressure and $V$ is the thermodynamic volume. Here, we give a geometrical description of this phase transition. Defining the relevant Legendre invariant thermogeometrics corresponding to the two criticality conditions, which determine the critical values of respective thermodynamical entities, we show that the critical point refers to the divergence of the Ricci scalars calculated from these metrics. The similar descriptions are also provided for the other two pictures of the van der Waals like phase transition: one is $T$-$S$ and the other one is $Y$-$X$ where $T$, $S$, $X$ and $Y$ are temperature, entropy, generalized force and generalized displacement; i.e. potential corresponding to external charge, respectively. The whole discussion is very general as no specific black hole metric is being used.

Minor modifications, to appear in Phys. Rev. D

References in corpus (16)

• Geometrothermodynamics
• Geometrothermodynamics of black holes
• Phase transition and Thermodynamical geometry of Reissner-Nordström-AdS Black Holes in Extended Phase Space
• Unified geometric description of black hole thermodynamics
• Geometric description of BTZ black holes thermodynamics
• Charged de Sitter-like black holes: quintessence-dependent enthalpy and new extreme solutions
• Thermogeometric phase transition in a unified framework
• Phase transition and critical phenomena of black holes: A general approach
• Continuous phase transition and critical behaviors of 3D black hole with torsion
• Phase transition and scaling behavior of topological charged black holes in Horava-Lifshitz gravity
• Thermal phase transitions of dimensionally continued AdS black holes
• Einstein-Maxwell-Dilatonic phantom black holes: Thermodynamics and geometrothermodynamics
• Homogeneity and thermodynamic identities in geometrothermodynamics
• Thermodynamic Volume and the Extended Smarr Relation
• Phantom black holes and critical phenomena
• A Hamiltonian approach for the Thermodynamics of AdS black holes

Cited by in corpus (45)

• Joule-Thomson expansion of charged Gauss-Bonnet black holes in AdS space
• P-V criticality of first-order entropy corrected AdS black holes in massive gravity
• Ruppeiner thermodynamic geometry for the Schwarzschild-AdS black hole
• Thermal Dynamic Phase Transition of Reissner-Nordström Anti-de Sitter Black Holes on Free Energy Landscape
• Van der Waals criticality in AdS black holes: a phenomenological study
• Novel phase transition in charged dilaton black holes
• Charged AdS black hole heat engines
• Extended black hole thermodynamics from extended Iyer-Wald formalism
• Thermodynamic geometry and interacting microstructures of BTZ black holes
• 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
• Geometrical thermodynamics and P-V criticality of charged accelerating AdS black holes
• Universality class of alternative phase space and Van der Waals criticality
• Black hole evaporation in Conformal (Weyl) gravity
• Novel relations in massive gravity at Hawking-Page transition
• Thermogeometric study of van der Waals like phase transition in black holes: an alternative approach
• Rényi Topology of Charged-flat Black Hole: Hawking-Page and Van-der-Waals Phase Transitions
• Thermodynamics and phase transition of charged AdS black holes with a global monopole
• The correspondence between thermodynamic curvature and isoperimetric theorem from ultraspinning black hole
• Rate of the phase transition for a charged anti-de Sitter black hole
• Diagnosis inspired by the thermodynamic geometry for different thermodynamic schemes of the charged BTZ black hole
• $Q$-$\Phi$ criticality and microstructure of charged AdS black holes in $f(R)$ gravity
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
• Divergence Behavior of Thermodynamic Curvature Scalar at Critical Point in the Extended Phase Space of Generic Black Holes
• Analytic Electrically Charged Black Holes in $F(R)$-ModMax Theory
• Thermodynamic curvature of AdS black holes with dark energy
• Phase Transitions and Critical Phenomena for the FRW Universe in an Effective Scalar-Tensor Theory
• Thermodynamic Curvature and Topological Insights of Hayward Black Holes with String Fluids
• Insight into the Microstructure of FRW Universe from a $P$-$V$ Phase Transition
• Microstructure and Continuous Phase Transition of the Gauss-Bonnet AdS Black Hole
• Quasinormal Modes and Van der Waals like phase transition of charged AdS black holes in Lorentz symmetry breaking massive gravity
• Revisiting thermodynamic topology of Hawking-Page and Davies type phase transitions
• On the thermodynamic phase structure of conformal gravity
• Fluid description of gravity on a timelike cut-off surface: beyond Navier-Stokes equation
• Thermodynamic and Holographic Information Dual to Volume
• Thermodynamics of bosonic systems in adS spacetime
• A new measure of thermal micro-behavior for the AdS black hole
• A note on the mass of Kerr-AdS black holes in the off-shell generalized ADT formalism
• Phase Transition of the Horava-Lifshitz AdS black holes
• Quantum State Dependence of Thermodynamic Phase Transition in 4D AdS Gauss-Bonnet Quantum Black Holes Surrounded With Cloud of Strings
• The role of the cosmological constant as a pressure in the (2+1)-dimensional black string
• Extended symmetry of the Maxwell theory with a gauge coupling constant as a conserved charge