Thermodynamical stability of $f(R)$-AdS black holes in grand canonical ensemble

Abstract

In this paper, $n$-dimensional ($n=4p,p$ is a positive integer) $f(R)$-AdS black holes is divided into Schwazschild-AdS (SAdS) like ones and Reissner-Nordström-AdS (RN-AdS) like ones. Thermodynamical stability of them in grand canonical ensemble is investigated. Locally, we find that the RN-AdS like $f(R)$ black holes will experience either type-one or type-two phase transitions from unstable states to stable states, whereas there are only type-two phase transitions between that two states for SAdS like $f(R)$ black holes. Globally, we find that there are type-one Hawking-Page like phase transitions between thermal AdS state and $f(R)$ black holes. Using thermodynamical geometry method, we find that thermodynamical extrinsic curvature can only provide accurate stability information near type-two (not type-one) phase transition points for $f(R)$ black holes in grand canonical ensemble.

arXiv comment9 pages

References in corpus (21)

• The Large N Limit of Superconformal Field Theories and Supergravity
• f(R) theories
• 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
• Reentrant Phase Transitions in Rotating AdS Black Holes
• Holographic Heat Engines
• Geometrothermodynamics
• Thermodynamics of Black Holes in Massive Gravity
• Thermal Fluctuations in a Charged AdS Black Hole
• Higher dimensional charged $f(R)$ black holes
• Photon orbits and thermodynamic phase transition of $d$-dimensional charged AdS black holes
• P-V criticality in AdS black holes of massive gravity
• Thermodynamics and Stability of Higher Dimensional Rotating (Kerr) AdS Black Holes
• Thermogeometric phase transition in a unified framework
• Extrinsic and intrinsic curvatures in thermodynamic geometry
• Chaos in charged AdS black hole extended phase space
• Configurational entropy of charged AdS black holes
• Phase transition and thermodynamic geometry of $f(R)$ AdS black holes in the grand canonical ensemble
• Phase transitions of black holes in massive gravity

Cited by in corpus (6)

• Dilaton black holes with power law electrodynamics
• Circular orbit of a test particle and phase transition of a black hole
• Charged accelerating black hole in $f(R)$ gravity
• Stability analysis on charged black hole with non-linear complex scalar
• Thermodynamics of BTZ Black Holes in Nonlinear Electrodynamics
• Thermal phase transition in $F(R)$-charged $Ad{S}_4$-scalar theory