Piotr Bizoń, Dominika Hunik-Kostyra, Maciej Maliborski
We consider the four-dimensional Einstein-Klein-Gordon-AdS system with conformal mass subject to the Robin boundary conditions at infinity. Above a critical value of the Robin parameter, at which the AdS spacetime goes linearly unstable, we prove existence of a family of globally regular static solutions (that we call AdS Robin solitons) and discuss their properties.
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We report on a series of new solutions to five-dimensional minimal supergravity. Our method applies to space-times with two commuting Killing symmetries and consists in combining dimensional reduction on two-spaces of constant curvature with reduction on a two-torus. The first gives rise to various generalized Bertotti-Robinson solutions supported by electric and magnetic fluxes, which presumably describe the near-horizon regions of black holes and black rings (strings). The second provides generating techniques based on U-duality of the corresponding three-dimensional sigma model. We identify…
Hairy black holes in AdS with Robin boundary conditions
研究四维渐近全局AdS时空中Robin边界条件下Einstein-Maxwell-complex scalar理论的毛黑洞，构建反反应几何并得到热AdS、RNAdS、带电玻色星与毛黑洞间相变且结构丰富的相图。
Quasinormal mode spectrum of the AdS black hole with the Robin boundary condition
本文研究具有Robin边界条件的渐近AdS黑洞标量场扰动的准正规模式谱，揭示边界条件驱动的不稳定性以及参数循环θ=0→2π下QNM谱的和乐性，其中第n泛音移动为第(n-1)泛音，基音被扫至复平面无穷远处。
It has been recently observed that a scalar field with Robin boundary conditions (RBCs) can trigger both a superradiant and a bulk instability for a BTZ black hole (BH). To understand the generality and scrutinize the origin of this behavior, we consider here the superradiant instability of a Kerr BH confined either in a mirror-like cavity or in AdS space, triggered also by a scalar field with RBCs. These boundary conditions are the most general ones that ensure the cavity/AdS space is an isolated system, and include, as a particular case, the commonly considered Dirichlet boundary conditions …
The AdS soliton is a nonsingular spacetime that has a flat conformal boundary with a compact $S^1$ direction. We find a horizonless cohomogeneity-1 metric that describes nonlinear gravitational oscillations of the AdS soliton in five dimensions. We call this spacetime the resonating AdS soliton. This solution is obtained as the nonlinear extension of normal modes of the AdS soliton dual to spin-2 glueball excitations. The boundary energy momentum tensor of the resonating AdS soliton has time periodic components, and it is interpreted as a coherently excited state in the dual field theory. Phys…
We investigate the behaviors of holographic entanglement entropy for AdS soliton geometries in the presence of higher derivative corrections. We calculate the leading higher derivative corrections for the AdS5 setup in type IIB string and for the AdS4,7 ones in M-theory. We also study the holographic entanglement entropy in Gauss-Bonnet gravity and study how the confinement/deconfinement phase transition observed in AdS solitons is affected by the higher derivative corrections.
We construct supersymmetric, asymptotically AdS$_5$ gravitational soliton solutions of five-dimensional gauged supergravity coupled to arbitrarily many vector multiplets. These generalize the supersymmetric solitons of $U(1)^3$ gauged supergravity previously constructed by Chong, Cvetic, Lu, and Pope. We show that the solitons contain evanescent ergosurfaces and give an argument that these solitons should be nonlinearly unstable.
We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate.
One more Sine-Gordon soliton in AdS
该论文在AdS时空中正弦-戈登理论的形变中，除已发现的平直空间对应单孤子解外，还找到了一个无平直空间对应物的新单孤子解。
In this work we study the phase transitions between the planar charged AdS black hole and the planar charged soliton. The planar soliton is obtained as a double analytic continuation of the charged black hole metric, which also involves analytically continuing the electric charge. We show that there are phase transitions between both solutions depending on the electric potential, magnetic flux and temperature. The analysis is carried out in the Grand-Canonical ensemble.
We study charged Dirac quasinormal modes (QNMs) on Reissner-Nordström-Anti-de Sitter (RN-AdS) black holes with generic Robin boundary conditions, by extending our earlier work of neutral Dirac QNMs on Schwarzschild-AdS black holes. We first derive the equations of motion for charged Dirac fields on a RN-AdS background. To solve these equations we impose a requirement on the Dirac field: that its energy flux should vanish at asymptotic infinity. A set of two Robin boundary conditions compatible with QNMs is consequently found. By employing both analytic and numeric methods, we then obtain the q…
We discuss electrostatics in Anti-de-Sitter ($AdS$) spacetime, in global coordinates. We observe that the multipolar expansion has two crucial differences to that in Minkowski spacetime. First, there are everywhere regular solutions, with finite energy, for every multipole moment except for the monopole. Second, all multipole moments decay with the same inverse power of the areal radius, $1/r$, as spatial infinity is approached. The first observation suggests there may be regular, self-gravitating, Einstein-Maxwell solitons in $AdS$ spacetime. The second observation, renders a Lichnerowicz-typ…
We construct new static, asymptotically AdS solutions where the conformal infinity is the product of Minkowski spacetime $M_n$ and a sphere $S^m$. Both globally regular, soliton-type solutions and black hole solutions are considered. The black holes can be viewed as natural AdS generalizations of the Schwarzschild black branes in Kaluza-Klein theory. The solitons provide new brane-world models with compact extra-dimensions. Different from the Randall-Sundrum single-brane scenario, a Schwarzschild black hole on the Ricci flat part of these branes does not lead to a naked singularity in the bulk…
In this paper, we reconsider the energy and tension laws of the Ricci flat black hole by taking the contribution of the tension term into account. After this considering and inspired by the interchange symmetry between the Ricci flat black hole and the AdS soliton solution which arises from the double analytic continuation of the time and compact spatial direction, we find out the analogy of the energy and tension laws of the AdS soliton solution. Moreover, we also investigate the energy and tension laws of the boosted Ricci flat black hole, and discuss the boosted AdS soliton solution. Howeve…
The Teukolsky master equation and its associated spin-weighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(-AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant boundary conditions. We find a set of two Robin boundary conditions (BCs) that must be imposed on the Teukolsky master variables to get perturbations that are asymptotically global AdS, i.e. that asymptotes to the Einstein Static Universe. In the context of the AdS/CFT correspondence, these BCs allow a no…
We investigate the marginally stable modes of the scalar (vector) perturbations in the AdS soliton background coupled to electric field. In the probe limit, we find that the marginally stable modes can reveal the onset of the phase transitions of this model. The critical chemical potentials obtained from this approach are in good agreement with the previous numerical or analytical results.
We explore the behaviour of charged scalar solitons in asymptotically global AdS4 spacetimes. This is motivated in part by attempting to identify under what circumstances such objects can become large relative to the AdS length scale. We demonstrate that such solitons generically do get large and in fact in the planar limit smoothly connect up with the zero temperature limit of planar scalar hair black holes. In particular, for given Lagrangian parameters we encounter multiple branches of solitons: some which are perturbatively connected to the AdS vacuum and surprisingly, some which are not. …
We show that in D=2n+1 dimensions, when mass is negative and all angular momenta are non-vanishing, Kerr and Kerr-AdS metrics describe smooth time machines, with no curvature singularity. Turning off the angular momenta appropriately can lead to static AdS solitons with negative mass. Setting zero the cosmological constant yields a class of Ricci-flat Kähler metrics in D=2n dimensions. We also show that Euclidean-signatured AdS solitons with negative mass can also arise in odd dimensions. We then construct time machines in D=5 minimal gauged supergravity that carry only magnetic dipole charges…
We analytically study the holographic superfluid phase transition in the AdS soliton background by using the variational method for the Sturm-Liouville eigenvalue problem. By investigating the holographic s-wave and p-wave superfluid models in the probe limit, we observe that the spatial component of the gauge field will hinder the phase transition. Moreover, we note that, different from the AdS black hole spacetime, in the AdS soliton background the holographic superfluid phase transition always belongs to the second order and the critical exponent of the system takes the mean-field value in …
Minimal $D=5$ supergravity admits asymptotically globally AdS$_5$ gravitational solitons (strictly stationary, geodesically complete spacetimes with positive mass). We show that, like asymptotically flat gravitational solitons, these solutions satisfy mass and mass variation formulas analogous to those satisfied by AdS black holes. A thermodynamic volume associated to the non-trivial topology of the spacetime plays an important role in this construction. We then consider these solitons within the holographic ``complexity equals action'' and ``complexity equals volume'' conjectures as simple ex…
We present a calculation of two-point correlation functions of the stress-energy tensor in the strongly-coupled, confining gauge theory which is holographically dual to the AdS soliton geometry. The fact that the AdS soliton smoothly caps off at a certain point along the holographic direction, ensures that these correlators are dominated by quasinormal mode contributions and thus show an exponential decay in position space. In order to study such a field theory on a curved spacetime, we foliate the six-dimensional AdS soliton with a Schwarzschild black hole. Via gauge/gravity duality, this new…
Phase Transitions and Stability of Eguchi-Hanson-AdS Solitons
本文研究了Eguchi-Hanson-AdS$_5$孤子时空的标量波方程模解，发现其具有正规模谱，并探讨了因果测地线、热力学性质及与AdS孤子的联系。
We construct a new class of Einstein-Maxwell static solutions with a magnetic field in $D$-dimensions (with $D\geq 5$ an odd number), approaching at infinity a globally Anti-de Sitter (AdS) spacetime. In addition to the mass, the new solutions possess an extra-parameter associated with a non-zero magnitude of the magnetic potential at infinity. Some of the black holes possess a non-trivial zero-horizon size limit, which corresponds to a solitonic deformation of the AdS background.
We investigate static, planar, solutions of Einstein-scalar gravity admitting an anti-de Sitter (AdS) vacuum. When the squared mass of the scalar field is positive and the scalar potential can be derived from a superpotential, minimum energy theorems indicate the existence of a scalar soliton. On the other hand, for these models, no-hair theorems forbid the existence of hairy black brane solutions with AdS asymptotics. By considering a specific example (an exact integrable model which has the form of a Toda molecule) and by deriving explicit exact solution, we show that these models allow for …
Normal modes of charged AdS solitons
本文研究四维和五维带电AdS孤子中的有质量带电标量场微扰，通过数值方法计算正则模谱，发现其频率为实数，表明孤子动态稳定，支持正能量猜想。
Perturbations of asymptotically Anti-de-Sitter (AdS) spacetimes are often considered by imposing field vanishing boundary conditions (BCs) at the AdS boundary. Such BCs, of Dirichlet-type, imply a vanishing energy flux at the boundary, but the converse is, generically, not true. Regarding AdS as a gravitational box, we consider vanishing energy flux (VEF) BCs as a more fundamental physical requirement and we show that these BCs can lead to a new branch of modes. As a concrete example, we consider Maxwell perturbations on Kerr-AdS black holes in the Teukolsky formalism, but our formulation appl…
The product space configuration $AdS_2\times S_2$ (with $l$ and $r$ being radiuses of the components) carrying the electric charge $Q$ is demonstrated to be an exact solution of the semiclassical Einstein equations in presence of the Maxwell field. If the logarithmic UV divergences are absent in the four-dimensional theory the solution we find is identical to the classical Bertotti-Robinson space ($r=l=Q$) with no quantum corrections added. In general, the analysis involves the quadratic curvature coupling $λ$ appearing in the effective action. The solutions we find are of the following types:…
We investigate the scalar perturbations in an AdS soliton background coupled to a Maxwell field via marginally stable modes. In the probe limit, we study the magnetic field effect on the holographic insulator/superconductor phase transition numerically and analytically. The condensate will be localized in a finite circular region for any finite constant magnetic field. Near the critical point, we find that there exists a simple relation among the critical chemical potential, magnetic field, the charge and mass of the scalar field. This relation indicates that the presence of the magnetic field…
Supersymmetric smooth distributions of M2-branes as AdS solitons
本文提出用沿紧致方向的 Wilson 圈消除 M2 膜分布奇点，得到光滑的超对称 AdS 孤子构型，并揭示其零温相图中相互关联的丰富相变结构。
We compute the quasinormal frequencies corresponding to the scalar sector of gravitational perturbations in the four-dimensional AdS-Schwarzschild black hole by using the master field formalism of hep-th/0305147. We argue that the non-deformation of the boundary metric favors a Robin boundary condition on the master field over the usual Dirichlet boundary condition mostly used in the literature. Using this Robin boundary condition we find a family of low-lying modes, whose frequencies match closely with predictions from linearized hydrodynamics on the boundary. In addition to the low-lying mod…
We study spherically symmetric soliton solutions in a model with a conformally coupled scalar field as well as in full conformal gravity. We observe that a new type of limiting behaviour appears for particular choices of the self-coupling of the scalar field, i.e. the solitons interpolate smoothly between the Anti-de Sitter vacuum and an uncharged configuration. Furthermore, within conformal gravity the qualitative approach of a limiting solution does not change when varying the charge of the scalar field - contrary to the Einstein-Hilbert case. However, it changes with the scalar self-couplin…
We first reconstruct the conserved (Abbott-Deser) charges in the spin connection formalism of gravity for asymptotically (Anti)-de Sitter spaces, and then compute the masses of the AdS soliton and the recently found Eguchi-Hanson solitons in generic odd dimensions, unlike the previous result obtained for only five dimensions. These solutions have negative masses compared to the global AdS or AdS/Z_p spacetimes. As a separate note, we also compute the masses of the recent even dimensional Taub-NUT-Reissner-Nordstrom metrics.
Electrostatics on global Anti-de-Sitter (AdS) spacetime is sharply different from that on global Minkowski spacetime. It admits a multipolar expansion with everywhere regular, finite energy solutions, for every multipole moment except the monopole (arXiv:1507.04370). A similar statement holds for global AdS magnetostatics. We show that everywhere regular, finite energy, electric plus magnetic fields exist on AdS in three distinct classes: $(I)$ with non-vanishing total angular momentum $J$; $(II)$ with vanishing $J$ but non-zero angular momentum density, $T^t_φ$; $(III)$ with vanishing $J$ and…
We study Lorentzian supersymmetric configurations in $D=4$ and $D=5$ gauged $\mathcal{N}=2$ supergravity. We show that there are smooth $1/2$ BPS solutions which are asymptotically AdS$_{4}$ and AdS$_{5}$ with a planar boundary, a compact spacelike direction and with a Wilson line on that circle. There are solitons where the $S^{1}$ shrinks smoothly to zero in the interior, with a magnetic flux through the circle determined by the Wilson line, which are AdS analogues of the Melvin fluxtube. There is also a solution with a constant gauge field, which is pure AdS. Both solutions preserve half of…
The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fails for the AdS soliton, a globally static, asymptotically toroidal $Λ<0$ spacetime with negative mass. Nonetheless, arguing from the AdS/CFT correspondence, Horowitz and Myers (hep-th/9808079) proposed a new positive energy conjecture, which asserts that the AdS soliton is the u…
We show that the gravitating static soliton in the 2+1 dimensional O(3) $σ$ model does not exist in the presence of a negative cosmological constant.
We describe a number of striking features of a class of smooth solitons in gauged and ungauged minimal supergravity in five dimensions. The solitons are globally asymptotically flat or asymptotically AdS without any Kaluza-Klein directions but contain a minimal sphere formed when a cycle pinches off in the interior of the spacetime. The solutions carry a local magnetic charge and many have rather unusual ergosurfaces. Perhaps most strikingly, many of the solitons have more electric charge or, in the asymptotically AdS case, more electric charge and angular momentum than is allowed by the usual…
Supersymmetric asymptotically locally AdS$_5$ gravitational solitons
本文利用 Gutowski-Reall 的 $SU(2)\times U(1)$ 不变 ansatz，构造了耦合任意向量多重态的五维规范超引力中完备、全局稳态的 $1/4$-BPS 渐近局部 AdS$_5$ 引力孤子。
We investigate the holographic p-wave superfluid in the background metric of the AdS soliton with $RF^{2}$ corrections. Two models, namely, the Maxwell complex vector field model and Yang-Mills theory, are studied in the above context by employing the Sturm-Liouville approach as well as the shooting method. When turning on the spatial components of the gauge field, one observes that, in the probe limit, the inclusion of $RF^{2}$ corrections hinders the superfluid phase transition. On the other hand, however, in the absence of the superfluid velocity, it is found that the $RF^2$ corrections lea…
Convexity restoration from hairy black hole in Einstein-Maxwell-charged scalar system in AdS
该研究在AdS时空中构建带电孤子解，发现毛黑洞解可恢复能量凸性，使相变连续化，并受AdS弱引力猜想影响。
Quantum-corrected three-dimensional AdS space-time
本文研究三维反德西特时空中的量子修正孤子，通过线性化量子修正爱因斯坦方程求解，并比较量子场论与相对论动力学理论计算的孤子质量。
We prove two theorems, announced in hep-th/0108170, for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifolds of non-negative Ricci curvature. For spacetimes with Ricci-flat conformal boundary, the convexity condition is associated with negative mass. The second theorem is a uniqueness theorem for the negative mass AdS soliton spacetime. This result lends support to the new positive …
Sine-Gordon solitons in AdS, dS and other hyperbolic spaces
研究在AdS、dS及双曲空间中发现正弦戈登理论的无限多孤子解及单孤子解，揭示其与超对称理论的关联及极限行为。
We derive new thermodynamic relations for asymptotically planar AdS black hole and soliton solutions. In addition to the ADM mass, these spacetimes are characterized by gravitational tensions in each of the planar spatial directions. We show that with planar AdS asymptotics, the sum of the ADM mass and tensions necessarily vanishes, as one would expect from the AdS /CFT correspondence. Each Killing vector of such a spacetime leads to a Smarr formula relating the ADM mass and tensions, the black hole horizon and soliton bubble areas, and a set of thermodynamic volumes that arise due to the non-…
We study the perturbation of the scalar field interacting with the Maxwell field in the background of d-dimensional charged AdS black hole and AdS soliton. Different from the single classical field perturbation, which always has the decay mode in the black hole background, we observe the possible growing mode when the perturbation of the scalar field strongly couples to the Maxwell field. Our results disclose the signature of how the phase transition happens when the interaction among classical fields is strong. The sudden change of the perturbation to growing mode is also observed in the AdS …
Thermodynamics of Chern-Simons AdS$_5$ black holes coupled to $\mathrm{SU}(2)$ solitons
本文研究了五维 Chern-Simons AdS 黑洞与 SU(2) 纠结子的性质，通过最小超空间近似方法，推导出作用量并确定守恒量及其共轭变量，验证了熵满足黑洞热力学第一定律。
We study static black hole solutions with locally spherical horizons coupled to non-Abelian field in $\mathcal{N}=4$ Chern-Simons AdS$_5$ supergravity. They are governed by three parameters associated to the mass, axial torsion and amplitude of the internal soliton, and two ones to the gravitational hair. They describe geometries that can be a global AdS space, naked singularity or a (non-)extremal black hole. We analyze physical properties of two inequivalent asymptotically AdS solutions when the spatial section at radial infinity is either a 3-sphere or a projective 3-space. An important fea…
We consider a real, massive scalar field both on the $n$-dimensional anti--de Sitter (AdS$_n$) spacetime and on its universal cover CAdS$_n$. In the second scenario, we extend the recent analysis on PAdS$_n$, the Poincaré patch of AdS$_n$, first determining all admissible boundary conditions of Robin type that can be applied on the conformal boundary. Most notably, contrary to what happens on PAdS$_n$, no bound state mode solution occurs. Subsequently, we address the problem of constructing the two-point function for the ground state satisfying the admissible boundary conditions. All these sta…
We consider solutions in Einstein-Maxwell theory with a negative cosmological constant that asymptote to global $AdS_{4}$ with conformal boundary $S^{2}\times\mathbb{R}_{t}$. At the sphere at infinity we turn on a space-dependent electrostatic potential, which does not destroy the asymptotic $AdS$ behaviour. For simplicity we focus on the case of a dipolar electrostatic potential. We find two new geometries: (i) an $AdS$ soliton that includes the full backreaction of the electric field on the $AdS$ geometry; (ii) a polarised neutral black hole that is deformed by the electric field, accumulati…
Quantum Solitons
本文研究了AdS_3中热场量子反作用的几何结构，通过四维AdS C度规中的膜构造出解，探讨了量子BTZ解与量子孤子解的热力学及第一定律。
By choosing an appropriate vielbein basis, we obtain a class of spherically-symmetric solutions in $f(T)$ gravities. The solutions are asymptotic to Minkowski spacetimes with leading falloffs the same as those of the Schwarzschild black hole. In general, these solutions have branch-cut singularities in the middle. For appropriately chosen $f(T)$ functions, extremal black holes can also emerge. Furthermore, we obtain wormhole configurations whose spatial section is analogous to an Ellis wormhole, but $-g_{tt}$ runs from 0 to 1 as the proper radial coordinate runs from $-\infty$ to $+\infty$. Th…
Eguchi-Hanson solitons are odd-dimensional generalizations of the four-dimensional Eguchi-Hanson metric and are asymptotic to AdS$_5$\mathbb{Z}_p$ when the cosmological constant is either positive or negative. We find soliton solutions to Lovelock gravity in 5 dimensions that are generalizations of these objects.
We study the stability of charged solitons in 5-dimensional Anti-de Sitter (AdS) space-time. We show that for appropriate choices of the parameters of the model these solutions become unstable to form scalar hair. We find that the existence of charged solitons with scalar hair depends crucially on the charge and the mass of the scalar field. We investigate the dependence of the spectrum of solutions on the mass of the scalar field in detail. For positive mass of the scalar field the hairy solitons can be interpreted as charged boson stars. We find that for sufficiently small value of the charg…
We explore the behaviors of the holographic superconductors at zero temperature for a charged scalar field coupled to a Maxwell field in higher-dimensional AdS soliton spacetime via analytical way. In the probe limit, we obtain the critical chemical potentials increase linearly as a total dimension $d$ grows up. We find that the critical exponent for condensation operator is obtained as 1/2 independently of $d$, and the charge density is linearly related to the chemical potential near the critical point. Furthermore, we consider a slightly generalized setup the Einstein-Power-Maxwell field the…
We study linear and nonlinear stability of asymptotically AdS$_4$ solutions in Einstein-Maxwell-scalar theory. After summarizing the set of static solutions we first examine thermodynamical stability in the grand canonical ensemble and the phase transitions that occur among them. In the second part of the paper we focus on nonlinear stability in the microcanonical ensemble by evolving radial perturbations numerically. We find hints of an instability corner for vanishingly small perturbations of the same kind as the ones present in the uncharged case. Collapses are avoided, instead, if the char…
We study chaotic motion of classical closed strings in the five-dimensional Anti-de Sitter (AdS) soliton spacetime. We first revisit classical chaos using a cohomogeneity-1 string ansatz. We then consider turbulent behaviors of the classical strings when the spatial dependence of the string world-sheet is included. Sensitivity to initial conditions in chaotic systems suggests that the string under chaos tends to stretch in the AdS soliton spacetime in a Lyapunov timescale. In this process, the orbital angular momentum transfers to internal spin due to the turbulence on the string. It follows t…
Einstein-scalar field solutions in AdS spacetime: clouds, boundary conditions, and scalar multipoles
本文研究了${\cal N}=8$ $D=4$规范超引力截断的Einstein-标量场模型，探讨了AdS时空中球对称孤子与黑洞解的渐近行为和边界条件，并发现了标量多极子孤子的精确解和数值解。
The behaviors of the holographic superconductors/insulator transition are studied by introducing a charged scalar field coupled with a logarithmic electromagnetic field in both the Einstein-Gauss-Bonnet AdS black hole and soliton. For the Einstein-Gauss-Bonnet AdS black hole, we find that: i) the larger coupling parameter of logarithmic electrodynamic field $b$ makes it easier for the scalar hair to be condensated; ii) the ratio of the gap frequency in conductivity $ω_g$ to the critical temperature $T_c$ depends on both $b$ and the Gauss-Bonnet constant $α$; and iii) the critical exponents are…
We analytically and numerically study quasinormal frequencies (QNFs) of neutral and charged scalar fields in the charged anti-de Sitter (AdS) black holes and discuss the stability of the black holes in terms of the QNFs. We focus on the range of the mass squared $μ^2$ of the scalar fields for which the Robin boundary condition parametrised by $ζ$ applies at the conformal infinity. We find that if the black hole of radius $r_{+}$ and charge $Q$ is much smaller than the AdS length $\ell$, the instability of the charged scalar field can be understood in terms of superradiance in the reflective bo…
Quantum-corrected anti-de Sitter space-time
本文研究量子标量场对四维整体AdS时空的反作用，通过数值求解量子修正爱因斯坦方程，发现偏离随温度升高而增大，并将量子修正度规解释为渐近AdS孤子，研究其质量与温度的关系。
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