Revisiting van der Waals like behavior of f(R) AdS black holes via the two point correlation function

Abstract

Van der Waals like behavior of $f(R)$ AdS black holes is revisited via two point correlation function, which is dual to the geodesic length in the bulk. The equation of motion constrained by the boundary condition is solved numerically and both the effect of boundary region size and $f(R)$ gravity are probed. Moreover, an analogous specific heat related to $\delta L$ is introduced. It is shown that the $T-\delta L$ graphs of $f(R)$ AdS black holes exhibit reverse van der Waals like behavior just as the $T-S$ graphs do. Free energy analysis is carried out to determine the first order phase transition temperature $T_{\ast }$ and the unstable branch in $T-\delta L$ curve is removed by a bar $T=T_{\ast }$. It is shown that the first order phase transition temperature is the same at least to the order of $10^{-10}$ for different choices of the parameter $b$ although the values of free energy vary with $b$. Our result further supports the former finding that charged $f(R)$ AdS black holes behave much like RN-AdS black holes. We also check the analogous equal area law numerically and find that the relative errors for both the cases ${\theta }_0=0.1$ and ${\theta }_0=0.2$ are small enough. The fitting functions between $\log \mid T-T_c\mid$ and $\log \mid \delta L-\delta L_c\mid$ for both cases are also obtained. It is shown that the slope is around 3, implying that the critical exponent is about $2/3$. This result is in accordance with those in former literatures of specific heat related to the thermal entropy or entanglement entropy.

arXiv commentRevised version. Match the published version. 14pages,5figures

References in corpus (56)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Extended Theories of Gravity
• P-V criticality of charged AdS black holes
• Charged AdS Black Holes and Catastrophic Holography
• Towards a derivation of holographic entanglement entropy
• Black hole chemistry: thermodynamics with Lambda
• Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes
• Entanglement Tsunami: Universal Scaling in Holographic Thermalization
• Thermalization of Strongly Coupled Field Theories
• Holographic Thermalization
• Holographic Particle Detection
• Black Holes in f(R) theories
• Black Hole Chemistry
• Static Spherically Symmetric Solutions in F(R) Gravity
• Higher dimensional charged $f(R)$ black holes
• Thermalization with a chemical potential from AdS spaces
• Palatini $f(R)$ Black Holes in Nonlinear Electrodynamics
• Introduction to Holographic Superconductor Models
• f(R) Black holes
• Black hole solutions in F(R) gravity with conformal anomaly
• Phase Transitions and Critical Behavior for Charged Black Holes
• $P-V$ criticality of AdS black hole in $f(R)$ gravity
• Van der Waals phase transition in the framework of holography
• Phase transition of holographic entanglement entropy in massive gravity
• Holographic Entanglement Entropy in Insulator/Superconductor Transition
• Black holes and Boyle's law -- the thermodynamics of the cosmological constant
• Instabilities and Anti-Evaporation of Reissner-Nordström Black Holes in modified $F(R)$ gravity
• Holographic Van der Waals-like phase transition in the Gauss-Bonnet gravity
• The relation between F(R) gravity and Einstein-conformally invariant Maxwell source
• Anti-Evaporation of Schwarzschild-de Sitter Black Holes in $F(R)$ gravity
• Holographic thermalization with a chemical potential in Gauss-Bonnet gravity
• Nonlocal probes of thermalization in holographic quenches with spectral methods
• Holographic Entanglement Entropy Close to Quantum Phase Transitions
• Thermodynamics and Entanglement Entropy with Weyl Corrections
• Holographic thermalization in Gauss-Bonnet gravity
• Holographic Signatures of Cosmological Singularities
• Stability of f(R) black holes
• Instability of rotating black hole in a limited form of $f(R)$ gravity
• Fidelity Susceptibility as Holographic PV-Criticality
• Black hole solutions in f(R) gravity coupled with non-linear Yang-Mills field
• Phase transitions and critical behavior of black branes in canonical ensemble
• An equal area law for holographic entanglement entropy of the AdS-RN black hole
• Holographic Thermalization and Generalized Vaidya-AdS Solutions in Massive Gravity
• Holographic thermalization and gravitational collapse in the spacetime dominated by quintessence dark energy
• Instability of a Kerr black hole in f(R) gravity
• A Rotating Charged Black Hole Solution in f(R) Gravity
• Time Evolution of Entanglement Entropy in Quenched Holographic Superconductors
• Stability analysis of f(R)-AdS black holes
• Coexistence curves and molecule number densities of AdS black holes in the reduced parameter space
• Holographic Thermalization in Charged Dilaton Anti-de Sitter Spacetime
• Holographic thermalization in noncommutative geometry
• Phase transition and thermodynamic geometry of $f(R)$ AdS black holes in the grand canonical ensemble
• Effect of phantom dark energy on the holographic thermalization

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• An alternative perspective to observe the critical phenomena of dilaton AdS black holes
• Holographic Entanglement Entropy and Van der Waals transitions in Einstein-Maxwell-dilaton theory
• Anti-de-Sitter-Maxwell-Yang-Mills black holes thermodynamics from nonlocal observables point of view
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