Narrow Results

A nontrivial scalar solution, whose source is a massive scalar field with a double-well potential, for a non-rotating Bananas–Teitelboim–Zanelli (BTZ) black hole is obtained with a condition , where μ is the mass of scalar field and the cosmological constant. The stability of solution is also studied. The mass of black hole with a scalar hair is greater than the black hole without hair. The scalar solution proposes a regular horizon which hides the naked singularity.

We study the gravity duals of striped holographic superconductors in the AdS black hole and AdS soliton backgrounds. We show the dependences of the condensation and the critical temperature/critical chemical potential on the inhomogeneity in these two different spacetimes. By exploring the dynamics of the normal phase through the scalar field perturbation, we argue that the pair susceptibility and the conductivity can be possible phenomenological indications to disclose the property of inhomogeneity.

In this paper, we present an exact spherically symmetric and Yang–Mills charged AdS black hole solution in the context of $4D$ Einstein–Gauss–Bonnet (EGB) gravity in the presence of a cloud of strings. The regularity of the solution is checked. Thermodynamics of this solution is studied. The critical behavior, the types of phase transitions in canonical ensemble, the Joule–Thomson expansion, the Clapeyron equation and the critical exponents shall be investigated.

In this paper, we applied AdS/CFT correspondence to carefully study images of quantum-corrected AdS black hole from the viewpoint of the wave optics. The result shows that the absolute amplitude of response function always displays an interference pattern that comes from the diffraction of the scalar wave. The strength of interference increases with quantum parameter a, while decreases with the event horizon $r_h$ and source parameters $(\omega ,\sigma )$. For the images of dual black hole, one can see at position ${\theta }_{\mathrm{\text{obs}}}=0$ that it is a perfect Einstein ring with a series of concentric striped patterns around it, while it will be broken at other positions. This result well coincides with the geometrical optics, i.e. the radius of ring. The feature of images of dual black hole is closely related to the parameters of black hole, source, and optics system. Especially, the effect of quantum parameter a on images of AdS black hole is very important. For instance, it gives rise to the fact that the image would evolve into one light spot at ${\theta }_{\mathrm{\text{obs}}}=\pi /2$, rather than two which is usually found in Schwarzschild AdS black hole. Finally, since the holographic images constructed from observables of the quantum system focus on testing the existence of dual black hole, we conclude that the holographic images of quantum corrected AdS black hole presented in this paper would be more helpful for this target.

We find new explicit solutions describing closed strings spinning with equal angular momentum in two independent planes in the AdS₅ black hole space–time. These are 2n-folded strings in the radial direction and also winding m times around an angular direction. We specially consider these solutions in the long string and high temperature limit, where it is shown that there is a logarithmic correction to the scaling between energy and spin. This is similar to the one-spin case. The strings are spinning, or actually orbiting around the black hole of the AdS₅ black hole space–time, similar to the solutions previously found in black hole space–times.

We investigate the analytical method in studying the holographic superfluid model which is described by Maxwell field minimally coupling to a charged scalar field in a fixed AdS black hole background. We propose a method that enables us to find exact value of coefficient in the solution and thus obtain higher-order expansion of the associated Landau free energy of the holographic superfluid with flow. We determine the critical value of superfluid velocity at the tricritical point of holographic superfluid and compare it with the numerical value.

The phase transition and critical behaviors of charged AdS black holes in $f(R)$ gravity with a conformally invariant Maxwell (CIM) source and constant curvature are further investigated. As a highlight, this research is carried out by employing new state parameters $(T,Q,\mathrm{\Phi })$ and contributes to deeper understanding of the thermodynamics and phase structure of black holes. Our analyses manifest that the charged $f(R)$-CIM AdS black hole undergoes a first-order small–large black hole phase transition, and the critical behaviors qualitatively behave like a Van der Waals liquid–vapor system. However, differing from the case in Einstein’s gravity, phase structures of the black holes in $f(R)$ theory exhibit an interesting dependence on gravity modification parameters. Moreover, we adopt the thermodynamic geometry to probe the black hole microscopic properties. The results show that, on the one hand, both the Ruppeiner curvature and heat capacity diverge exactly at the critical point, on the other hand, the $f(R)$-CIM AdS black hole possesses the property as ideal Fermi gases. Of special interest, we discover a microscopic similarity between the black holes and a Van der Waals liquid–vapor system.

Thermodynamical properties of charged AdS black holes with a global monopole still remain obscure. In this paper, we investigate the thermodynamics and phase transition of the black holes in the extended phase space. It is shown that thermodynamical quantities of the black holes exhibit an interesting dependence on the internal global monopole, and they perfectly satisfy both the first law of thermodynamics and Smarr relation. Furthermore, analysis of the local and the global thermodynamical stability manifests that the charged AdS black hole undergoes an elegant phase transition at critical point. Of special interest, critical behaviors of the black holes resemble a Van der Waals liquid–gas system. Our results not only reveal the effect of a global monopole on thermodynamics of AdS black holes, but also further support that Van der Waals-like behavior of the black holes is a universal phenomenon.

We investigate the relations between the black hole shadow and charged AdS black hole critical behavior in the extended phase space. Using the thermo-shadow formalism built in Ref. 1, we reveal that the shadow radius can be considered as an efficient tool to study thermodynamical black hole systems. Based on such arguments, we build a thermal profile by varying the RN–AdS black hole temperature on the shadow silhouette. Among others, the Van der Waals-like phase transition takes place. This could open a new window on the thermal picture of black holes and the corresponding thermodynamics from the observational point of view.

In this paper, we investigate the thermodynamical phase transitions of the spherically symmetric AdS black hole in Horava–Lifshitz (HL) gravity for the detailed balance violation parameter $0\le {ϵ}^2\le 1$. First, by calculating the HP temperature $T_{\mathrm{\text{HP}}}$, the minimum temperature $T_{\mathrm{\text{min}}}$ and the Gibbs free energy $G$ of the AdS black hole in different values of parameter $ϵ$, we find that the HP phase transition can occur at all pressures. Comparing the HP temperature $T_{\mathrm{\text{HP}}}$ with the minimum temperature $T_{\mathrm{\text{min}}}$, we notice that the ratio of $T_{\mathrm{\text{HP}}}/T_{\mathrm{\text{min}}}$ tends to 1 when $d\to \infty$. Second, for the small–large black hole phase transition of the AdS black hole, we discover that the black hole heat capacity is divergent at the minimum temperature $T_{\mathrm{\text{min}}}$, the small–large black hole phase transition occurs at the same time. Furthermore, the black hole entropy also exists $S_{\mathrm{\text{HP}}}$ when $T=T_{\mathrm{\text{HP}}}$, and $S_{\mathrm{\text{min}}}$ when the black hole temperature has its minimum $T_{\mathrm{\text{min}}}$, we surprisingly find that the ratio of $S_{\mathrm{\text{HP}}}/S_{\mathrm{\text{min}}}$ tends to $e$ when the dimension $d\to \infty$, which provides a general relation between the Hawking–Page phase transition and the small–large black hole phase transition of the AdS black hole in the large dimension. All in all, the ratios of typical temperature and entropy of two kinds of phase transitions tend to natural constant in the large dimension limit, which may imply to understand the nature of two different phase transitions.

In this paper, we analyze the $P-v$ criticality and the heat engine efficiency of two black holes, one is the four-dimensional charged AdS black hole in Rastall gravity and the other is the four-dimensional charged AdS black hole surrounded by quintessence in Rastall gravity. For the four-dimensional charged AdS black hole in Rastall gravity, the ratio $\frac{P_c{\upsilon }_c}{T_c}$ is related to the Rastall parameter $\lambda$. When $\lambda =0$ the ratio becomes $\frac{P_c{v}_c}{T_c}=\frac{3}{8}$, which is same as the van der Waals liquid-gas system. Additionally, as the Rastall parameter $\lambda$ increases, the heat engine efficiency $\eta$ of the black hole will increase. Moreover, the efficiency $\eta$ decreases rapidly at first and then increases with the entropy $S_2$. But the efficiency ratio $\frac{\eta }{{\eta }_c}$ decreases with the Rastall parameter $\lambda$. For the four-dimensional charged AdS black hole surrounded by quintessence in Rastall gravity, as the charge q increases, the critical specific volume ${\upsilon }_c$ and the efficiency ratio $\frac{P_c{\upsilon }_c}{T_c}$ also increase, however, the critical temperature $T_c$ and the critical pressure $P_c$ gradually decrease. Moreover, the heat engine efficiency $\eta$ and the efficiency ratio $\frac{\eta }{{\eta }_c}$ of the black hole are similar to the four-dimensional charged AdS black hole in Rastall gravity.

In the present paper, we consider the bouncing braneworld scenario, in which the bulk is given by a five-dimensional charged AdS black hole space–time with matter field confined in a D₃ brane. Then, we study the stability of solutions with respect to homogeneous and isotropic perturbations. Specifically, the AdS black hole with zero ADM mass and charge, and open horizon is an attractor, while the charged AdS black hole with zero ADM mass and flat horizon, is a repeller.

We study the time evolution of the Misner-Sharp mass and the apparent horizon for gravitational collapse of a massless scalar field in the $Ad{S}_5$ spacetime for both cases of narrow and broad waves by numerically solving the Einstein’s equations coupled to a massless scalar field. This is done by relying on the full dynamics of the collapse including the concept of the dynamical horizon. It turns out that the Misner-Sharp mass is everywhere constant except for a rapid change across a thin shell defined by the density profile of the collapsing wave. By studying the evolution of the apparent horizon, indicating the formation of a black hole at different times we see how asymptotically an event horizon forms. The dependence of the thermalization time on the radius of the initial black hole event horizon is also studied.

In this work, we study the phase transition of the charged-AdS black hole surrounded by quintessence via an alternative extended phase space defined by the charge square $Q^2$ and her conjugate $\mathrm{\Psi }$, a quantity proportional to the inverse of horizon radius, while the cosmological constant is kept fixed. The equation of state is derived under the form $Q^2=Q^2(T,\mathrm{\Psi })$ and the critical behavior of such black hole analyzed. In addition, we examine the role of the quintessence parameter and its effects on phase transitions. Besides that, we explore the connection between the microscopic structure and Ruppeiner geothermodynamics. We also find that, at certain points of the phase space, the Ruppeiner curvature is characterised by the presence of singularities that are interpreted as a signal of the occurrence of the phase transitions.

In this work, we examine the Joule–Thomson (JT) expansion for a nonlinearly charged AdS black hole solution. We obtain the expression of the JT coefficient from which we calculate the inversion temperature for numerous values of the charge $Q$. Moreover, we derive the isenthalpic curve in $(T,P)$ diagram and illustrate the cooling–heating region by the inversion curve for fixed masses. We find that the temperature and pressure on the inversion point decrease with a larger charge $Q$ and increase as the black hole mass grows.