Critical behaviour of Lifshitz dilaton black holes

Abstract

Till now, critical behaviour of Lifshitz black holes, in an extended $P-v$ space, has not been studied, because it is impossible to find an analytical equation of state, $P=P(v,T)$, for an arbitrary Lifshitz exponent $z$. In this paper, we adopt a new approach toward thermodynamic phase space and successfully explore the critical behaviour of $(n+1)$-dimensional Lifshitz dilaton black holes. For this purpose, we write down the equation of state as $Q^s=Q^s(T,\Psi )$ with $\Psi ={\left(\partial M/\partial Q^s\right)}_{S,P}$ is the conjugate of $Q^s$ and construct Smarr relation based on this new phase space as $M=M(S,Q^s,P)$, where $s=2p/(2p-1)$ with $p$ is the power of the power-law Maxwell Lagrangian. We justify such a choice mathematically and show that with this new phase space, the system admits the critical behaviour and resembles the Van der Waals fluid system when the cosmological constant (pressure) is treated as a fixed parameter, while the charge of the system varies. We obtain Gibbs free energy of the system and find swallow tail shape in Gibbs diagrams which represents the first order phase transition. Finally, we calculate the critical exponents and show that although thermodynamic quantities depend on the metric parameters such as $z$ , $p$ and $n$, the critical exponents are the same as Van der Walls fluid-gas system. This alternative viewpoint toward phase space of lifshitz dilaton black hole can be understood easily since one can imagine such a change for a given single black hole i.e., acquiring charge which induces the phase transition. Our results further support the viewpoint suggested in \cite{Dehy}.

arXiv comment14 pages

References in corpus (52)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Building an AdS/CFT superconductor
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• P-V criticality of charged AdS black holes
• Charged AdS Black Holes and Catastrophic Holography
• Enthalpy and the Mechanics of AdS Black Holes
• AdS/CFT Correspondence and Symmetry Breaking
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Holographic Superconductors
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Adding flavor to AdS/CFT
• Gravity Duals of Lifshitz-like Fixed Points
• Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes
• Correlation functions in the CFT(d)/AdS(d+1) correpondence
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization
• More on a holographic dual of QCD
• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Pressure and volume in the first law of black hole thermodynamics
• The cosmological constant and the black hole equation of state
• Multiple Reentrant Phase Transitions and Triple Points in Lovelock Thermodynamics
• Extended phase space thermodynamics and P-V criticality of black holes with nonlinear source
• Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes
• Critical behavior of Born-Infeld AdS black holes in the extended phase space thermodynamics
• Black holes in asymptotically Lifshitz spacetime
• Compressibility of rotating black holes
• Symmetry Breaking Using Value Precedence
• Black holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent
• P-V Criticality of Topological Black Holes in Lovelock-Born-Infeld Gravity
• Mechanical First Law of Black Hole Spacetimes with Cosmological Constant and Its Application to Schwarzschild-de Sitter Spacetime
• Black holes and black branes in Lifshitz spacetimes
• Critical behavior of charged Gauss-Bonnet AdS black holes in the grand canonical ensemble
• Critical phenomena in Born-Infeld AdS black holes
• Critical behaviour and microscopic structure of charged AdS black holes via an alternative phase space
• Critical behavior of Born Infeld AdS black holes in higher dimensions
• P-V criticality of charged dilatonic black holes
• $P-V$ criticality and geometrothermodynamics of black holes with Born-Infeld type nonlinear electrodynamics
• Thermodynamics of black branes in asymptotically Lifshitz spacetimes
• Thermodynamics of topological nonlinear charged Lifshitz black holes
• Reentrant phase transition of Born-Infeld-AdS black holes
• Mass and Thermodynamic Volume in Lifshitz Spacetimes
• Critical behaviors and phase transitions of black holes in higher order gravities and extended phase spaces
• Novel phase transition in charged dilaton black holes
• Critical behavior and phase transition of dilaton black holes with nonlinear electrodynamics
• The Extended Thermodynamic Phase Structure of Taub-NUT and Taub-Bolt
• Critical behavior of Born-Infeld dilaton black holes
• Thermodynamics, phase transitions and Ruppeiner geometry for Einstein-dilaton Lifshitz black holes in the presence of Maxwell and Born-Infeld electrodynamics
• The Extended Thermodynamic Properties of Taub-NUT/Bolt-AdS spaces
• Gravitational Tension, Spacetime Pressure and Black Hole Volume
• Thermodynamics of Gauss-Bonnet-Dilaton Lifshitz Black Branes

Cited by in corpus (14)

• Thermodynamic topology of Phantom AdS Black Holes in Massive Gravity
• Microstructure of charged AdS black hole via $P-V$ criticality
• Critical behavior of Gauss-Bonnet black holes via an alternative phase space
• Alternative approach to the critical behavior and microscopic structure of the power-Maxwell black holes
• Universal thermodynamic topological classes of static black holes in Conformal Killing Gravity
• Phase transition and entropic force of de Sitter black hole in massive gravity
• Static spherically symmetric Einstein-Yang-Mills-dilaton black hole and its thermodynamics
• Critical behavior of charged dilaton black holes in AdS space
• Hawking Radiation and $P-v$ Criticality of Charged Dynamical (Vaidya) Black Hole in Anti-de Sitter Space
• Critical Behaviour and Microscopic Structure of Charged AdS Black Hole with a Global Monopole in Extended and Alternate Phase Spaces
• Scalar fields and Lifshitz black holes from Derrick's theorem evasion
• Thermodynamics and reentrant phase transition for logarithmic nonlinear charged black holes in massive gravity
• Lifshitz and hyperscaling violated Yang-Mills-dilaton black holes
• Charged dilaton black hole with multiple Liouville potentials and gauge fields