Ruppeiner thermodynamic geometry for the Schwarzschild-AdS black hole

Abstract

Due to the non-independence of entropy and thermodynamic volume for spherically symmetric black holes in the AdS spacetime, when applying the Ruppeiner thermodynamic geometry theory to these black holes, we often encounter an unavoidable problem of the singularity about the line element of thermodynamic geometry. In this paper, we propose a basic and natural scheme for dealing with the thermodynamic geometry of spherically symmetric AdS black holes. We point out that enthalpy, not internal energy, is the fundamental thermodynamic characteristic function for the Ruppeiner thermodynamic geometry. Based on this fact, we give the specific forms of the line element of thermodynamic geometry for Schwarzschild AdS (SAdS) black hole in different phase spaces and the results show that the thermodynamic curvatures obtained in different phase spaces are equivalent. It is shown that the thermodynamic curvature is negative which implies that the attractive interaction dominates between black hole molecules for the SAdS black hole. Meanwhile we also give an approximate expression of the thermodynamic curvature of the Schwarzschild black hole which indicates that the black hole is dominated by repulsion on low temperature region and by attraction on high temperature region.

arXiv commentv1:5 pages, twocolumn, 2 figures; v2:add References and some comments, published in Physical Review D

References in corpus (32)

• P-V criticality of charged AdS black holes
• Enthalpy and the Mechanics of AdS Black Holes
• Thermodynamical Aspects of Gravity: New insights
• Black hole chemistry: thermodynamics with Lambda
• Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes
• The Thermodynamics of Black Holes
• Pressure and volume in the first law of black hole thermodynamics
• The cosmological constant and the black hole equation of state
• Insight into the Microscopic Structure of an AdS Black Hole from Thermodynamical Phase Transition
• Repulsive Interactions and Universal Properties of Charged Anti-de Sitter Black Hole Microstructures
• Black Hole Thermodynamics
• Thermodynamic curvature and phase transitions in Kerr-Newman black holes
• Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes
• Phase transition and Thermodynamical geometry of Reissner-Nordström-AdS Black Holes in Extended Phase Space
• Thermodynamic Curvature of the BTZ Black Hole
• Ruppeiner Geometry, Phase Transitions, and the Microstructure of Charged AdS Black Holes
• Holographic entanglement entropy and the extended phase structure of STU black holes
• Thermodynamic curvature measures interactions
• Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in $Ad{S}_5\times S^5$ spacetime
• Thermodynamic curvature and black holes
• Thermodynamical Metrics and Black Hole Phase Transitions
• On thermal molecular potential among micromolecules in charged AdS black holes
• Intriguing microstructures of five-dimensional neutral Gauss-Bonnet AdS black hole
• Thermogeometric description of the van der Waals like phase transition in AdS black holes
• Thermodynamic Volumes for AdS-Taub-NUT and AdS-Taub-Bolt
• A general framework to study the extremal phase transition of black holes
• Thermodynamics and Phase Transition of a Gauss-Bonnet Black Hole in a Cavity
• Interaction potential and thermo-correction to the equation of state for thermally stable Schwarzschild Anti-de Sitter black holes
• Thermogeometric study of van der Waals like phase transition in black holes: an alternative approach
• Thermodynamic Instabilities of Generalized Exotic BTZ Black Holes
• The intrinsic curvature of thermodynamic potentials for black holes with critical points
• Geometric thermodynamics: black holes and the meaning of the scalar curvature

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• Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space
• Thermodynamic geometry for charged Gauss-Bonnet black holes in AdS spacetimes
• Thermal Dynamic Phase Transition of Reissner-Nordström Anti-de Sitter Black Holes on Free Energy Landscape
• Novel dual relation and constant in Hawking-Page phase transitions
• Thermodynamic geometry and interacting microstructures of BTZ black holes
• Ruppeiner Geometry, Phase Transitions and Microstructures of Black Holes in Massive Gravity
• $P-v$ criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics
• Phase structure of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state
• Ruppeiner Geometry, Reentrant Phase transition and Microstructure of Born-Infeld AdS Black Hole
• Microstructure of charged AdS black hole via $P-V$ criticality
• The emergence of universal relations in the AdS black holes thermodynamics
• Fokker-Planck equation for black holes in thermal potential
• Black Hole Chemistry: the first 15 years
• Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity
• Novel relations in massive gravity at Hawking-Page transition
• Fine micro-thermal structures for Reissner-Nordström black hole
• The correspondence between thermodynamic curvature and isoperimetric theorem from ultraspinning black hole
• Universal criticality of thermodynamic curvatures for charged AdS black holes
• Rate of the phase transition for a charged anti-de Sitter black hole
• van der Waals fluid and charged AdS black hole in the Landau theory
• Diagnosis inspired by the thermodynamic geometry for different thermodynamic schemes of the charged BTZ black hole
• Ruppeiner curvature along a renormalization group flow
• Topology of black hole thermodynamics via Rényi statistics
• Phase Transition Dynamics of Black Holes Influenced by Kaniadakis and Barrow Statistics
• Hawking Radiation and $P-v$ Criticality of Charged Dynamical (Vaidya) Black Hole in Anti-de Sitter Space
• Thermodynamics curvature in phase transitions for AdS black hole
• AdS black hole thermodynamics and microstructures from $f(Q)$ gravitation
• Ruppeiner Geometry of the RN-AdS Black Hole Using Shadow Formalism
• Generalized Maxwell equal area law and black holes in complex free energy
• Thermodynamic curvature of AdS black holes with dark energy
• 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
• Thermodynamic curvature of the Schwarzschild-AdS black hole and Bose condensation
• Phase structures and critical behaviour of rational non-linear electrodynamics AdS black holes in Rastall gravity
• Thermodynamic geometry and phase transition of spinning AdS black holes
• Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space
• Interaction Between AdS Black Hole Molecules
• Can we know about black hole thermodynamics through shadows?
• Geometry of AdS black hole thermodynamics in extended phase space
• Overview of thermodynamic properties for Reissner-Nordstrom-de Sitter spacetime in induced phase space
• Can shadows connect black hole microstructures?
• Kramer's Escape Rate and Phase Transition Dynamics in AdS Black Holes
• Microstructure of Charged AdS Black Hole with Minimal Length Effects
• Thermodynamic bounce effect in quantum BTZ black hole
• Topological black holes in Einstein-Maxwell and 4D conformal gravities revisited
• A new measure of thermal micro-behavior for the AdS black hole
• The Kramers escape rate of phase transitions for the 6-dimensional Gauss-Bonnet AdS black hole with triple phases
• Ruppeiner geometry, P-V criticality and interacting microstructures of black holes in dRGT massive gravity
• The radial distribution function reveals the underlying mesostructure of the AdS black hole
• Topological Signatures and Geometrothermodynamics of Critical Phenomena in Regularized Maxwell Black Holes
• Information geometry and Bose-Einstein condensation