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

Abstract

It is well-known that the non-extremal anti-de-Sitter (AdS) black holes show various van der Waals type criticalities, such as the $P-V$, $T-S$, $Y-X$, $Q^2-\Psi$ etc. In these cases, the phase space diagram of the relevant quantities are similar in behaviour to the isotherms on $P-V$ diagram for the usual van der Waals gas system. The existing thermogeometric descriptions of these criticalities for the black holes deal with the whole thermogeometric manifold and its curvature. However, while observing the criticality, one only notices the behaviour of the relevant phase space variables and keep all other thermodynamic quantities as fixed. Therefore it is quite natural to investigate the geometrical behaviour of the induced metric, defined by these constant macroscopic variables, corresponding to the whole manifold of the thermogeometry. Using geometrothermodynamics (GTD), we precisely address this issue. It is observed that the extrinsic curvature of this induced metric also diverges at the critical point. This provides an alternative but important aspect of the thermogeometric description of phase transition of black holes. The entire formalism in this paper is very general as it is valid for any arbitrary black hole which shows the van der Waals type phase transition.

arXiv commentA few comments added, to appear in Phys. Lett. B

References in corpus (59)

• P-V criticality of charged AdS black holes
• Charged AdS Black Holes and Catastrophic Holography
• Enthalpy and the Mechanics of AdS Black Holes
• Black hole chemistry: thermodynamics with Lambda
• Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes
• Pressure and volume in the first law of black hole thermodynamics
• The cosmological constant and the black hole equation of state
• Geometrothermodynamics
• Compressibility of rotating black holes
• Geometry of black hole thermodynamics
• Thermodynamic Geometry and Critical Behavior of Black Holes
• Geometrothermodynamics of black holes
• Phase transition and Thermodynamical geometry of Reissner-Nordström-AdS Black Holes in Extended Phase Space
• Thermodynamic Curvature of the BTZ Black Hole
• On the Thermodynamic Geometry of BTZ Black Holes
• Critical phenomena in Born-Infeld AdS black holes
• Geometrothermodynamics of asymptotically anti - de Sitter black holes
• A new approach toward geometrical concept of black hole thermodynamics
• Critical behaviour and microscopic structure of charged AdS black holes via an alternative phase space
• Critical behavior of Born Infeld AdS black holes in higher dimensions
• Where is the PdV term in the first law of black hole thermodynamics?
• 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
• Charged BTZ black holes in the context of massive gravity's rainbow
• Quantum gravity effects on Hořava-Lifshitz black hole
• Unified geometric description of black hole thermodynamics
• Holographic Van der Waals-like phase transition in the Gauss-Bonnet gravity
• Geometric description of BTZ black holes thermodynamics
• Van der Waals criticality in AdS black holes: a phenomenological study
• Thermodynamic geometry of a black hole surrounded by perfect fluid in Rastall theory
• Quantum corrections to thermodynamics of quasitopological black holes
• Thermogeometric description of the van der Waals like phase transition in AdS black holes
• Thermal fluctuations of charged black holes in gravity's rainbow
• Thermal Fluctuations in a Hyperscaling Violation Background
• Leading-order corrections to charged rotating AdS black holes thermodynamics
• Hyperscaling violating black holes with spherical and hyperbolic horizons
• Thermogeometric phase transition in a unified framework
• Logarithmic corrected Van der Waals black holes in higher dimensional AdS space
• Phase transition of charged black holes in massive gravity through new methods
• Phase transition and critical phenomena of black holes: A general approach
• Continuous phase transition and critical behaviors of 3D black hole with torsion
• Extrinsic and intrinsic curvatures in thermodynamic geometry
• Phase transition and scaling behavior of topological charged black holes in Horava-Lifshitz gravity
• Ruppeiner geometry and 2D dilaton gravity in the thermodynamics of black holes
• A general framework to study the extremal phase transition of black holes
• Thermal fluctuations to thermodynamics of non-rotating BTZ black hole
• Black Hole Enthalpy and Scalar Fields
• Thermal phase transitions of dimensionally continued AdS black holes
• Universality class of alternative phase space and Van der Waals criticality
• Geometrothermodynamics of phantom AdS black holes
• Einstein-Maxwell-Dilatonic phantom black holes: Thermodynamics and geometrothermodynamics
• $Q-\Phi$ criticality in the extended phase space of $(n+1)$-dimensional RN-AdS black holes
• Homogeneity and thermodynamic identities in geometrothermodynamics
• Maxwell's equal area law for charged Anti-deSitter black holes
• Phantom black holes and critical phenomena
• Phase transitions, geometrothermodynamics and critical exponents of black holes with conformal anomaly
• A consistent and unified picture for critical phenomena of $f(R)$ AdS black holes
• Fundamentals of Geometrothermodynamics

Cited by in corpus (14)

• 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
• Topological interpretation of extremal and Davies-type phase transitions of black holes
• Thermal Stability, P-V Criticality and Heat Engine of Charged Rotating Accelerating Black Holes
• Fokker-Planck equation for black holes in thermal potential
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
• Critical Phenomena and Reentrant Phase Transition of Asymptotically Reissner-Nordstrom Black Holes
• Microstructure and Continuous Phase Transition of the Gauss-Bonnet AdS Black Hole
• Revisiting thermodynamic topology of Hawking-Page and Davies type phase transitions
• Exploring the Effects of Generalized Entropy onto Bardeen Black Hole Surrounded by Cloud of Strings
• A new measure of thermal micro-behavior for the AdS 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
• Thermodynamics and optical aspects of ModMax black holes in higher order curvature gravity with quintessence dark energy