Holographic Brownian motion in 2+1 dimensional hairy black holes

In this paper, we investigate the dynamics of a heavy quark for plasmas corresponding to three dimensional hairy black holes. We utilize the AdS/CFT correspondence to study the holographic Brownian motion of this particle with different kinds of hairy black holes. For an uncharged black hole in the low frequency limit we derive analytic expressions for the correlation functions and the response functions and verify that the fluctuation–dissipation theorem holds in the presence of a scalar field against a metric background. In the case of a charged black hole, we think that the results are similar to that derived for an uncharged black hole.     

$$$$-Dimensional charged black holes with scalar hair in Einstein–Power–Maxwell Theory

In \((2+1)\)-dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter \(k=1\) and \(k\ne 1\)), in the Einstein–Power–Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with \(k\ne 1\), we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.     

Holographic superconductors in the AdS black-hole spacetime with a global monopole

We study holographic superconductors in the Schwarzschild–AdS black hole with a global monopole through a charged complex scalar field. We calculate the condensates of the charged operators in the dual conformal field theories (CFTs) and discuss the effects of the global monopole on the condensation formation. Moreover, we compute the electric conductive using the probe approximation and find that the properties of the conductive are quite similar to those in the Schwarzschild–AdS black hole. These results can help us know more about holographic superconductors in the asymptotic AdS black holes.     

Diffusion Constant and Shear Viscosity in the Charged 3D Hairy Black Hole

A charged hairy black hole in 3 dimensions considered to study hydrodynamics. Specially, we calculate diffusion constant and obtain the effect of black hole electric charge and scalar charge on it. This parameter help us to obtain information about black hole and will be useful to study shear viscosity of dual picture by using AdS/CFT.     

Abundant stable gauge field hair for black holes in anti-de Sitter space

We present new hairy black hole solutions of SU(N) Einstein-Yang-Mills (EYM) theory in asymptotically anti-de Sitter (AdS) space. These black holes are described by N+1 independent parameters and have N-1 independent gauge field degrees of freedom. Solutions in which all gauge field functions have no zeros exist for all N, and for a sufficiently large (and negative) cosmological constant. At least some of these solutions are shown to be stable under classical, linear, spherically symmetric perturbations. Therefore there is no upper bound on the amount of stable gauge field hair with which a black hole in AdS can be endowed.     

Double‐trace deformations and entanglement entropy in AdS

We compute the bulk entanglement entropy of a massive scalar field in a Poincare AdS with the Dirichlet and Neumann boundary condition when we trace out a half space. Moreover, by taking into account the quantum back reaction to the minimal surface area, we calculate how much the entanglement entropy changes under a double‐trace deformation of a holographic CFT. In the AdS3/CFT2 setup, our result agrees with the known result in 2d CFTs. In higher dimensions, our results offer holographic predictions.     

Statistical entropies of extremal Kaluza-Klein AdS black holes in arbitrary dimensions

We have investigated the microscopic interpretations of the entropies for the four-dimensional extremal Kaluza-Klein AdS black hole and its higher-dimensional generalizations by using the Kerr/CFT correspondence. These newly-found Kaluza-Klein AdS black holes are charged rotating asymptotically AdS black hole solutions of gauged supergravity in four and higher dimensions. With suitable boundary conditions on the perturbations of the near-horizon geometry, it is shown that the asymptotic symmetry generators form a two-dimensional Virasoro algebra with a central term. By utilizing the central charge and the temperature of the dual conformal field theory, Cardy formula reproduces the expected Bekenstein-Hawking entropy. Directly working on the ordinary metrics of the extremal Kaluza-klein AdS black holes without taking the near-horizon limit, we also re-derive their microscopic entropies.     

Dynamical perturbations and critical phenomena in Gauss–Bonnet AdS black holes

We investigate the perturbations of charged scalar field in 5-dimensional Gauss–Bonnet AdS black hole backgrounds. From the perturbation behaviors we obtain the objective picture on how the high curvature influences the spacetime perturbation and the condensation of the scalar hair. The high curvature effects can also be read from the linear response function such as the susceptibility and the correlation length, when the system approaches the critical point. We find that the Gauss–Bonnet term does not affect the critical exponents of the system and they still take the mean-field values.     

Solenoid Configurations and Gravitational Free Energy of the AdS–Melvin Spacetime

In this paper we explore a solenoid configuration involving a magnetic universe solution embedded in an empty Anti-de Sitter (AdS) spacetime. This requires a non-trivial surface current at the interface between the two spacetimes, which can be provided by a charged scalar field. When the interface is taken to the AdS boundary, we recover the full AdS–Melvin spacetime. The stability of the AdS–Melvin solution is also studied by computing the gravitational free energy from the Euclidean action.     

Validity of thermodynamic laws and weak cosmic censorship for AdS black holes and black holes in a cavity

By throwing a test charged particle into a Reissner-Nordstrom (RN) black hole, we test the validity of the first and second laws of thermodynamics and the weak cosmic censorship conjecture (WCCC) with two types of boundary conditions: the asymptotically anti-de Sitter (AdS) space and a Dirichlet cavity wall placed in an asymptotically flat space. For the RN-AdS black hole, the second law of thermodynamics is satisfied, and the WCCC is violated for both extremal and near-extremal black holes. For the RN black hole in a cavity, the entropy can either increase or decrease depending on the change in the charge, and the WCCC is satisfied/violated for the extremal/near-extremal black hole. Our results indicate that there may be a connection between the black hole thermodynamics and the boundary condition imposed on the black hole.     

Kaluza–Klein reductions and AdS/Ricci-flat correspondence

The AdS/Ricci-flat (AdS/RF) correspondence is a map between families of asymptotically locally AdS solutions on a torus and families of asymptotically flat spacetimes on a sphere. The aim of this work is to perturbatively extend this map to general AdS and asymptotically flat solutions. A prime application for such map would be the development of holography for Minkowski spacetime. In this paper we perform a Kaluza–Klein (KK) reduction of AdS on a torus and of Minkowski on a sphere, keeping all massive KK modes. Such computation is interesting on its own, as there are relatively few examples of such explicit KK reductions in the literature. We perform both KK reductions in parallel to illustrate their similarity. In particular, we show how to construct gauge invariant variables, find the field equations they satisfy, and construct a corresponding effective action. We further diagonalize all equations and find their general solution in closed form. Surprisingly, in the limit of large dimension of the compact manifolds (torus and sphere), the AdS/RF correspondence maps individual KK modes from one side to the other. In a sequel of this paper we will discuss how the AdS/RF maps acts on general linear perturbations.     

Conformally coupled scalars, instantons, and vacuum instability in 4D anti-de Sitter space

We show that a scalar field conformally coupled to AdS gravity in four dimensions with a quartic self-interaction can be embedded into M theory. The holographic effective potential is exactly calculated, allowing us to study nonperturbatively the stability of AdS4 in the presence of the conformally coupled scalar. It is shown that there exists a one-parameter family of conformal scalar boundary conditions for which the boundary theory has an unstable vacuum. In this case, the bulk theory has instanton solutions that mediate the decay of the AdS4 space. These results match nicely with the vacuum structure and the existence of instantons in an effective three-dimensional boundary model.     

Casimir Effect for Concentric Spheres in de Sitter Spacetime with Signature Change

We revisit the Casimir effect for two concentric spherical shells in de Sitter background with a new geometric configuration, namely Euclidean signature between and Lorentzian signature outside the spheres with different cosmological constants, for a massless scalar field satisfying Dirichlet boundary conditions on the spheres. It is shown that an extra constant pressure emerges due to this signature changing configuration. Some interesting aspects of this extra term are then discussed.     

Gauged Kaluza-Klein AdS pseudo-supergravity

We obtain the pseudo-supergravity extension of the D-dimensional Kaluza-Klein theory, which is the circle reduction of pure gravity in D+1 dimensions. The fermionic partners are pseudo-gravitino and pseudo-dilatino. The full Lagrangian is invariant under the pseudo-supersymmetric transformation, up to quadratic order in fermion fields. We find that the theory possesses a U(1) global symmetry that can be gauged so that all the fermions are charged under the Kaluza-Klein vector. The gauging process generates a scalar potential that has a maximum, leading to the AdS vacuum. Whist the highest dimension for gauged AdS supergravity is seven, our gauged AdS pseudo-supergravities can exist in arbitrary dimensions.     

Lifshitz时空s波超导模型的关联长度和穿透深度

在D=d+2维各向异性的Lifshitz黑洞时空背景中, 在探子极限下, 用解析方法研究了临界温度附近引力系统的微扰, 计算出超导的关联长度ξα(1/T_c)(1-(T/T_c)^-1/2, 这与平均场论的结果一致. 进一步, 考虑在该系统中加一个均匀外磁场, 计算出穿透深度λα(T_c-T)^-1/2, 该结果与Ginzburg-Landau理论相符.     

Universality and a generalized C-function in CFTs with AdS duals

We argue that the thermodynamics of conformal field theories with AdS duals exhibits a remarkable universality. At strong coupling, a Cardy–Verlinde entropy formula holds even when R-charges or bulk supergravity scalars are turned on. In such a setting, the Casimir entropy can be identified with a generalized C-function that changes monotonically with temperature as well as when non-trivial bulk scalar fields are introduced. We generalize the Cardy–Verlinde formula to cases where no subextensive part of the energy is present and further observe that such a formula is valid for the super Yang–Mills theory in D=4 even at weak coupling. Finally we show that a generalized Cardy–Verlinde formula holds for asymptotically flat black holes in any dimension.     

On AdS/QCD correspondence and the partonic picture of deep inelastic scattering

We critically examine the question of scaling of the Deep Inelastic Scattering process in the medium Bjorken x region on a scalar boson in the framework of the AdS/QCD correspondence. To get the right polarization structure of the forward electroproduction amplitude, we show that one needs to add (at least) the scalar to scalar and scalar to vector hadronic amplitudes. This illustrates how the partonic picture may emerge from a simple scenario based on the AdS/QCD correspondence, provided one allows the conformal dimension of the hadronic field to equal 1 and use the concept of “hadron–parton duality”.     

Scalar filed evolution and area spectrum for Lovelock-AdS black holes

We study the modes of evolution of massless scalar fields in the asymptotically AdS spacetime surrounding maximally symmetric black holes of large and intermediate size in the Lovelock model. It is observed that all modes are purely damped at higher orders. Also, the rate of damping is seen to be independent of order at higher dimensions. The asymptotic form of these frequencies for the case of large black holes is found analytically. Finally, the area spectrum for such black holes is found from these asymptotic modes.     

Holographic superconductor in the analytic hairy black hole

We study the charged black hole of hyperbolic horizon with scalar hair (charged Martinez-Troncoso-Zanelli: CMTZ black hole) as a model of analytic hairy black hole for holographic superconductor. For this purpose, we investigate the second order phase transition between CMTZ and hyperbolic Reissner-Nordström-AdS (HRNAdS) black holes. However, this transition unlikely occurs. As an analytic treatment for holographic superconductor, we develop superconductor in the bulk and superfluidity on the boundary using the CMTZ black hole below the critical temperature. The presence of charge destroys the condensates around the zero temperature, which is in accord with the thermodynamic analysis of the CMTZ black hole.     

Remark on the variational principle in the AdS/CFT correspondence for the scalar field

We discuss how the variational principle can be used as a criterion for choosing, among scalar field actions implying the same equation of motion, the appropriate one for the AdS/CFT correspondence.