$Q$-$\Phi$ criticality and microstructure of charged AdS black holes in $f(R)$ gravity

Abstract

The phase transition and critical behaviours of charged AdS black holes in $f(R)$ gravity with a conformally invariant Maxwell (CIM) source and constant curvature are further investigated. As a highlight, this research is carried out by employing new state parameters $(T,Q,\Phi )$ and contributes to deeper understanding the thermodynamics and phase structure of black holes. Our analyses manifest that the charged $f(R)$-CIM AdS black hole undergoes a first order small-large black hole phase transition, and the critical behaviours qualitatively behave like a Van der Waals liquid-vapor system. However, differing from the case in Einstein's gravity, phase structures of the black holes in $f(R)$ theory exhibit an interesting dependence on gravity modification parameters. Moreover, we adopt the thermodynamic geometry to probe the black hole microscopic properties. The results show that, on the one hand, both the Ruppeiner curvature and heat capacity diverge exactly at the critical point, on the other hand, the $f(R)$-CIM AdS black hole possesses the property as ideal Fermi gases. Of special interest, we discover a microscopic similarity between the black holes and a Van der Waals liquid-vapor system.

arXiv comment17 pages, 12 figures

References in corpus (58)

• f(R) Theories Of Gravity
• 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
• Enthalpy and the Mechanics of AdS Black Holes
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Thermodynamics of Kerr-Newman-AdS Black Holes and Conformal Field Theories
• Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes
• Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization
• The Thermodynamics of Black Holes
• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Pressure and volume in the first law of black hole thermodynamics
• Phases of R-charged Black Holes, Spinning Branes and Strongly Coupled Gauge Theories
• P-V criticality in the extended phase space of Gauss-Bonnet black holes in AdS space
• Extended Gravity Theories and the Einstein-Hilbert Action
• Insight into the Microscopic Structure of an AdS Black Hole from Thermodynamical Phase Transition
• Extended phase space thermodynamics and P-V criticality of black holes with nonlinear source
• Inflation and quintessence with nonminimal coupling
• Black Holes in f(R) theories
• Critical behavior of Born-Infeld AdS black holes in the extended phase space thermodynamics
• Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes
• Geometry of Higher-Dimensional Black Hole Thermodynamics
• Higher dimensional charged $f(R)$ black holes
• Holographic entanglement entropy and the extended phase structure of STU black holes
• New type of phase transition in Reissner Nordström - AdS black hole and its thermodynamic geometry
• On Thermodynamics of AdS Black Holes in Arbitrary Dimensions
• Thermodynamic curvature measures interactions
• Critical phenomena of static charged AdS black holes in conformal gravity
• Thermodynamics of phase transition in higher dimensional AdS black holes
• Ruppeiner Geometry of RN Black Holes: Flat or Curved?
• P-V criticality of charged dilatonic black holes
• Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in $Ad{S}_5\times S^5$ spacetime
• Dilatonic BTZ black holes with power-law field
• Thermodynamic Geometry and Phase Transitions in Kerr-Newman-AdS Black Holes
• Correspondence of phase transition points and singularities of thermodynamic geometry of black holes
• Holographic Van der Waals-like phase transition in the Gauss-Bonnet gravity
• Cosmology Based on f(R) Gravity Admits 1 eV Sterile Neutrinos
• The relation between F(R) gravity and Einstein-conformally invariant Maxwell source
• Ehrenfest's scheme and thermodynamic geometry in Born-Infeld AdS black holes
• P-V criticality in AdS black holes of massive gravity
• Thermogeometric description of the van der Waals like phase transition in AdS black holes
• Thermodynamic geometry of black holes in f(R) gravity
• A unified phase transition picture of the charged topological black hole in Horava-Lifshitz gravity
• The Extended Thermodynamic Phase Structure of Taub-NUT and Taub-Bolt
• Existence condition and phase transition of Reissner-Nordström-de Sitter black hole
• Generalised Smarr Formula and the Viscosity Bound for Einstein-Maxwell-Dilaton Black Holes
• Stability analysis of f(R)-AdS black holes
• Thermodynamics and Thermodynamic geometry of Park black hole
• The fate of Schwarzschild-de Sitter Black Holes in $f(R)$ gravity
• $Q-\Phi$ criticality in the extended phase space of $(n+1)$-dimensional RN-AdS black holes
• Thermodynamics and Hawking radiation of five-dimensional rotating charged Gödel black holes
• Thermodynamic Geometry and Topological Einstein-Yang-Mills Black Holes
• Hawking radiation of charged rotating AdS black holes in conformal gravity for charged massive particles, complex scalar and Dirac particles
• A unified thermodynamic picture of Hořava-Lifshitz black hole in arbitrary space time
• Thermodynamic Geometry and Phase Transitions of AdS Braneworld Black Holes

Cited by in corpus (17)

• Ruppeiner Geometry, Phase Transitions, and the Microstructure of Charged AdS Black Holes
• Thermodynamic geometry for charged Gauss-Bonnet black holes in AdS spacetimes
• Intriguing microstructures of five-dimensional neutral Gauss-Bonnet AdS black hole
• Thermodynamic geometry and interacting microstructures of BTZ black holes
• Ruppeiner Geometry, Phase Transitions and Microstructures of Black Holes in Massive Gravity
• Ruppeiner Geometry, Reentrant Phase transition and Microstructure of Born-Infeld AdS Black Hole
• Thermodynamic Black Holes
• Repulsive Interactions in the Microstructure of Regular Hayward Black Hole in Anti-de Sitter Spacetime
• Phase transition and microstructures of five-dimensional charged Gauss-Bonnet-AdS black holes in the grand canonical ensemble
• Coexistent Physics and Microstructure of the Regular Bardeen Black Hole in Anti-de Sitter Spacetime
• AdS black hole thermodynamics and microstructures from $f(Q)$ gravitation
• The extended uncertainty principle effects on the phase transitions of Reissner-Nordström and Schwarzschild black holes
• Microstructure and continuous phase transition of a regular Hayward black hole in anti-de Sitter spacetime
• Thermodynamics of charged AdS black holes in rainbow gravity
• Ruppeiner geometry, P-V criticality and interacting microstructures of black holes in dRGT massive gravity
• Thermodynamics, photon sphere and thermodynamic geometry of Ayón-Beato-García Spacetime
• Effects of global monopole on critical behaviors and microstructure of charged AdS black holes