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Register a new userMicrostructure of charged AdS black hole via $P-V$ criticality
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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.
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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.
As is well known that RN-AdS black hole has a phase transition which is similar to that of van der Waals 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 this basis, we introduce a new order parameter and use the Landau continuous phase transition theory to discuss the critical phenomenon of RN-AdS black hole and give the critical exponent. By constructing the binary fluid model of black hole molecules, we investigate the microstructure of black holes. Furthermore, by studying the effect of the spacetime scalar curvature on the phase transition, we find that the charged and uncharged molecules of black holes are with different microstructure red which is like fermion gas and boson gas.
In this paper, we analytically study the critical exponents and universal amplitudes of the thermodynamic curvatures such as the intrinsic and extrinsic curvature at the critical point of the small-large black hole phase transition for the charged AdS black holes. At the critical point, it is found that the normalized intrinsic curvature $R_N$ and extrinsic curvature $K_N$ has critical exponents 2 and 1, respectively. Based on them, the universal amplitudes $R_Nt^2$ and $K_Nt$ are calculated with the temperature parameter $t=T/T_c-1$ where $T_c$ the critical value of the temperature. Near the critical point, we find that the critical amplitude of $R_Nt^2$ and $K_Nt$ is $-frac{1}{2}$ when $trightarrow0^+$, whereas $R_Nt^2approx -frac{1}{8}$ and $K_Ntapprox-frac{1}{4}$ in the limit $trightarrow0^-$. These results not only hold for the four dimensional charged AdS black hole, but also for the higher dimensional cases. Therefore, such universal properties will cast new insight into the thermodynamic geometries and black hole phase transitions.
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.
We study the P-V criticality and phase transition in the extended phase space of charged anti-de Sitter black holes in canonical ensemble of ghost-free massive gravity, where the cosmological constant is viewed as a dynamical pressure of the black hole system. We give the generalized thermodynamic first law and the Smarr relation with massive gravity correction. We find that not only when the horizon topology is spherical but also in the Ricci flat or hyperbolic case, there appear the P-V criticality and phase transition up to the combination k+c02c2m2 in the four-dimensional case, where k characterizes the horizon curvature and c2m2 is the coefficient of the second term of massive potential associated with the graviton mass. The positivity of such combination indicate the van der Waals-like phase transition. When the spacetime dimension is larger then four, the Maxwell charge there seems unnecessary for the appearance of critical behavior, but a infinite repulsion effect needed, which can also be realized through negative valued c3m2 or c4m2, which is third or fourth term of massive potential. When c3m2 is positive, a Hawking-Page-like black hole to vacuum phase transition is shown in the five-dimensional chargeless case. For the van der Waals-like phase transition in four and five spacetime dimensions, we calculate the critical exponents near the critical point and find they are the same as those in the van der Waals liquid-gas system.
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