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Register a new userThermal chaos of a charged dilaton-AdS black hole in the extended phase space
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We have studied thermal chaotic behavior in the extended phase space for a charged dilaton-AdS black hole by Melnikov method and present the effect of dilaton parameter on the thermal chaos. Our result show that for the temporal perturbation the thermal chaos in the charged dilaton-AdS black hole occurs only if the perturbation amplitude is larger than certain a critical value, but for the spatially perturbation, the chaos always exists irrespective of perturbation amplitude. These behaviors are similar to those in other AdS black hole, which can be regarded as the common features of the static AdS black holes. Moreover, we also find that the critical temporal perturbation amplitude leading to chaos increases with the dilaton parameter and decreases with the charge. This means that under the temporal perturbation the presence of dilaton parameter makes the onset of chaos more difficult, which differs from that of the charge parameter.
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We study the $P-V$ criticality and phase transition in the extended phase space of charged Gauss-Bonnet black holes in anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black hole. The black holes can have a Ricci flat ($k=0$), spherical ($k=1$), or hyperbolic ($k=-1$) horizon. We find that for the Ricci flat and hyperbolic Gauss-Bonnet black holes, no $P-V$ criticality and phase transition appear, while for the black holes with a spherical horizon, even when the charge of the black hole is absent, the $P-V$ criticality and the small black hole/large black hole phase transition will appear, but it happens only in $d=5$ dimensions; when the charge does not vanish, the $P-V$ criticality and the small black hole/large phase transition always appear in $d=5$ dimensions; in the case of $dge 6$, to have the $P-V$ criticality and the small black hole/large black hole phase transition, there exists an upper bound for the parameter $b=widetilde{alpha}|Q|^{-2/(d-3)}$, where $tilde {alpha}$ is the Gauss-Bonnet coefficient and $Q$ is the charge of the black hole. We calculate the critical exponents at the critical point and find that for all cases, they are the same as those in the van der Waals liquid-gas system.
Previously, the Maxwell equal-area law has been used to discuss the conditions satisfied by the phase transition of charged AdS black holes with cloud of string and quintessence, and it was concluded that black holes have phase transition similar to that of vdW system. The phase transition depends on the electric potential of the black hole and is not the one between a large black hole and a small black hole. On the basis of this result, we study the relation between the latent heat of the phase transition and the parameter of dark energy, and use the Landau continuous phase transition theory to discuss the critical phenomenon of the black hole with quintessence and give the critical exponent. By introducing the number density of the black hole molecules, some properties of the microstructure of black holes are studied in terms of a phase transition. It is found that the electric charge of the black hole and the normalization parameter related to the density of quintessence field play a key role in phase transition. By constructing the binary fluid model of the black hole molecules, we also discuss the microstructure of charged AdS black holes with a cloud of strings and quintessence.
Using Maxwells equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black holes with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in $P-v$ diagrams. The two-phase equilibrium curves in $P-T$ diagrams are plotted, and we take the first order approximation of volume $v$ in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for higher dimensional charged topological black hole with a nonlinear source. The latent heat of isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phases coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems.
We suggest a new thermodynamic curvature, constructed via adiabatic compressibility, for examining the internal microstructure of charged black holes in an anti-de Sitter (AdS) background. We analyze the microscopic properties of small-large phase transition of black holes with pressure and volume as the fluctuation variables. We observe that strong repulsive interactions dominate among the micro-structures of near extremal small black holes, and the thermodynamic curvature diverges to positive infinity for the extremal black holes. At the critical point, however, thermodynamic curvature diverges to negative infinity.
By introducing the general construction of Landau free energy of the van der Waals system and charged AdS black hole system, we have preliminarily realized the Landau continuous phase transition theory in black hole thermodynamics. The results show that the Landau free energy constructed in present paper can directly reflect the physical process of black hole phase transition. Specifically, the splitting of the global minimum of the Landau free energy corresponds to the second-order phase transition of the black hole, and the transformation of the global minimum reflects the first-order phase transition of the black hole.
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