Validity of Maxwell Equal Area Law for Black Holes Conformally Coupled to Scalar Fields in ${\text{AdS}}_5$ Spacetime

Abstract

We investigate the $P-V$ criticality and the Maxwell equal area law for a five-dimensional spherically symmetric AdS black hole with a scalar hair in the absence of and in the presence of a Maxwell field, respectively. Especially in the charged case, we give the exact $P-V$ critical values. More importantly, we analyze the validity and invalidity of the Maxwell equal area law for the AdS hairy black hole in the scenarios without and with charges, respectively. Within the scope of validity of the Maxwell equal area law, we point out that there exists a representative van der Waals-type oscillation in the $P-V$ diagram. This oscillating part that indicates the phase transition from a small black hole to a large one can be replaced by an isobar. The small and large black holes share the same Gibbs free energy. We also give the distribution of the critical points in the parameter space both without and with charges, and obtain for the uncharged case the fitting formula of the co-existence curve. Meanwhile, the latent heat is calculated, which gives the energy released or absorbed between the small and large black hole phases in the isothermal-isobaric procedure.

v1: 20 pages, 3 figures; v2: clarifications and references added; v3: 22 pages, 2 tables, 5 figures, clarifications added; v4: 23 pages, 6 figures, clarifications on the negative entropy added, final version to appear in Eur. Phys. J. C

References in corpus (11)

• Building an AdS/CFT superconductor
• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Clapeyron equations and fitting formula of the coexistence curve in the extended phase space of charged AdS black holes
• Critical behavior of charged black holes in Gauss-Bonnet gravity`s rainbow
• Thermodynamics and Entanglement Entropy with Weyl Corrections
• Phase transition and critical phenomena of black holes: A general approach
• The different phases of hairy black holes in AdS5 space
• Vacuum energy and the latent heat of AdS-Kerr black holes
• Thermodynamics of Horndeski black holes with non-minimal derivative coupling
• Black hole thermodynamics, conformal couplings, and R^2 terms
• Phase transition and entropy inequality of noncommutative black holes in a new extended phase space

Cited by in corpus (17)

• Microstructure and continuous phase transition of RN-AdS black hole
• On thermal molecular potential among micromolecules in charged AdS black holes
• Hawking Radiation of Five-dimensional Charged Black Holes with Scalar Fields
• Microscopic structures and thermal stability of black holes conformally coupled to scalar fields in five dimensions
• Joule-Thomson expansion for the regular(Bardeen)-AdS black hole
• Continuous phase transition and microstructure of charged AdS black hole with quintessence
• Novel equal area law and analytical charge-electric potential criticality for charged Anti-de Sitter black holes
• Recovery of consistency in thermodynamics of regular black holes in Einstein's gravity coupled with nonlinear electrodynamics
• On some phase equilibrium features of charged black holes in flat spacetime via Rényi statistics
• Dynamic Property of Phase Transition for Non-Linear Charged Anti-de Sitter black holes
• Critical Phenomena and Reentrant Phase Transition of Asymptotically Reissner-Nordstrom Black Holes
• Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space
• Phase transition of non-linear charged Anti-de Sitter black holes
• Black hole solutions in theory of ModMax-dRGT-like massive gravity
• Overview of thermodynamic properties for Reissner-Nordstrom-de Sitter spacetime in induced phase space
• On heat properties of charged AdS black holes in Gauss-Bonnet gravity coupled with nonlinear electrodynamics
• Phantom BTZ black holes