Previous work on the AdS instability problem within the two-time framework (TTF) has found an "oscillating singularity" whose presence depends on the gauge choice. We give a physical interpretation of this singularity as a diverging redshift between the boundary and the center of AdS. This signals a genuine breakdown of the linearized gravity. One can also identify the diverging redshift through a back-reaction calculation purely in the boundary gauge, where the TTF result stays regular.
We study thermodynamic and classical instability of AdS black holes in fourth-order gravity. These include the BTZ black hole in new massive gravity, Schwarzschild-AdS black hole, and higher-dimensional AdS black holes in fourth-order gravity. All thermodynamic quantities which are computed using the Abbot-Deser-Tekin method are used to study thermodynamic instability of AdS black holes. On the other hand, we investigate the $s$-mode Gregory-Laflamme instability of the massive graviton propagating around the AdS black holes. We establish the connection between the thermodynamic instability and…
We argue that if the degeneracy of the spectrum of linear perturbations of AdS is properly taken into account, there are globally regular, time-periodic, asymptotically AdS solutions (geons) bifurcating from each linear eigenfrequency of AdS.
We consider five-dimensional, vacuum Einstein equations with negative cosmological constant within cohomogenity-two biaxial Bianchi IX ansatz. This model allows to investigate the stability of AdS without adding any matter to the energy-momentum tensor, thus analyzing instability of genuine gravtational degrees of freedom. We derive the resonant system and identify vanishing secular terms. The results resemble those obtained for Einstein equations coupled to a spherically-symmetric, massless scalar field, backing the evidence that the scalar field model captures well the relevant features of A…
We consider the intermediate and end state behavior of the superradiantly perturbed Kerr black hole. Superradiant scattering in an asymptotically flat background is considered first. The case of a Kerr black hole in an Anti de-Sitter background is then discussed. Specifically we review what is known about the superradiant instability arising in AdS and its possible end state behavior.
The Anti-de Sitter (AdS) black hole with lattice structure plays an essential role in the study of the optical conductivity in holographic approach. We investigate the instability of this sort of black holes which may lead to the holographic description of charge density waves. In the presence of homogeneous axion fields, we show that the instability of AdS-Reissner-Nordström(AdS-RN) black hole is always suppressed. However, in the presence of Q-lattices, we find that the unstable region becomes the smallest in the vicinity of the critical region for metal/insulator phase transition. This nove…
We study the stability of extreme Reissner-Nordström-AdS black hole under massless scalar perturbations. We show that the perturbation on the horizon of the extreme Reissner-Nordström-AdS black hole experiences a power-law decay, instead of an exponential decay as observed in the nonextreme AdS black hole. On the horizon of the extreme Reissner-Nordström-AdS black hole, the blow up happens at lower order derivative of the scalar field compared with that of the extreme Reissner-Nordström black hole, which shows that extreme AdS black holes tend to instability in comparison to black holes in asy…
We study the phenomena of superradiance for $F(R)$-Maxwell black holes in an AdS space-time. The AdS boundary plays the role of a mirror and provides a natural confining system that makes the superradiant waves bouncing back and forth between the region near the horizon and the reflective boundary, causing a possible superradiant instability. We obtain numerical solutions for static hairy black holes in this scenario and investigate their instability and explicitly address the stability of such solutions for spherical perturbations under specific conditions for the scalar charge and AdS radius…
In this work, we analyze the necessary conditions for a nonlinear AdS-type instability in the gravity-scalar field system. In particular, we discuss the necessary conditions for a cascade of energy to higher modes by applying results in KAM theory. Our analytical framework explains numerical observations of instability of spacetimes even when the spectrum is only asymptotically resonant, and the fact that a minimum field amplitude is needed to trigger it. Our framework can be applied for similar stability analyses of fields in (locally) asymptotically AdS spacetimes. We illustrate this with th…
We investigate the stability of $D$ dimensional singly rotating Myers-Perry-AdS black holes under superradiance against scalar field perturbations. It is well known that small four dimensional rotating or charged Anti-de Sitter (AdS) black holes are unstable against superradiance instability of a scalar field. Recent works extended the existence of this instability to five dimensional rotating charged AdS black holes or static charged AdS black holes in arbitrary dimensions. In this work we analytically prove that, rotating small AdS black holes in arbitrary dimensions also show superradiance …
We consider the problem of stability of anti-de Sitter spacetime in five dimensions under small purely gravitational perturbations satisfying the cohomogeneity-two biaxial Bianchi IX ansatz. In analogy to spherically symmetric scalar perturbations, we observe numerically a black hole formation on the time-scale $\mathcal{O}(\varepsilon^{-2})$, where $\varepsilon$ is the size of the perturbation.
The superradiant instability of Kerr-AdS black holes is studied by numerically solving the full 3+1 dimensional Einstein equations. We find that the superradiant instability results in a two stage process with distinct initial and secondary instabilities. At the end of the secondary instability the geometry oscillates at several distinct fundamental frequencies -- a multi-oscillating black hole. The multi-oscillating black hole is remarkably close to a black resonator, albeit with a bit of gravitational hair. During the hairy black resonator epoch, the evolution of the horizon area is consiste…
We study the effect of R**2 term to the modulated instability in the U(1) charged black hole in five-dimensional Anti-de Sitter space-time. We consider the first-order corrections of R**2 term to the background and the linear order perturbations in the equations of motion. From the analysis, we clarify the effect of R**2 term in the modulated instability, and conclude that fluctuations are stable in the whole bulk in the range of values the coefficient of R**2 term can take.
We study the instability of a Reissner-Nordström-AdS (RNAdS) black hole under perturbations of a massive scalar field coupled to Einstein tensor. Calculating the potential of the scalar perturbations we find that as the strength of the coupling of the scalar to Einstein tensor is increasing, the potential develops a negative well outside the black hole horizon, indicating an instability of the background RNAdS. We then investigate the effect of this coupling on the quasinormal modes. We find that there exists a critical value of the coupling which triggers the instability of the RNAdS. We also…
We study the instability of small AdS black holes with two independent rotation parameters in minimal five-dimensional gauged supergravity to massless scalar perturbations. We analytically solve the Klein-Gordon equation for low-frequency perturbations in two regions of the spacetime of these black holes: namely, in the region close to the horizon and in the far-region. By matching the solutions in an intermediate region, we calculate the frequency spectrum of quasinormal modes. We show that in the regime of superradiance only the modes of even orbital quantum number undergo negative damping, …
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…
Is it possible the no-hair paradigm is violated when a black hole undergoes an instability? Employing massless charged scalar perturbations, we address this question within the context of conformally invariant Einstein-Maxwell theory for some allowed $d$-dimensional ($d=4n+4$ with conformal parameter $n=0,1,2,...$ ) topological small AdS black-holes. We provide numerical analyses that show the non trivial scalar hairy black hole solutions to include planar and spherical horizon topologies in higher dimensions with an even conformal parameter $n$. It is also shown that the solutions presented h…
We study the pathologies in AdS black branes in Lovelock theory. More precisely, we examine the conditions that AdS black branes have the naked singularity, the ghost instability and the dynamical instability. From the point of view of the AdS/CFT correspondence, the pathologies in AdS black branes indicate the pathologies in the corresponding CFT. Hence, we need to be careful when we apply AdS/CFT in Lovelock theory to various phenomena such as the shear viscosity to entropy ratio in strongly coupled quantum filed theory.
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 non-perturbatively the stability of AdS_4 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 AdS_4 space. These results match nicely with the va…
We numerically construct asymptotically anti-de Sitter (AdS) black holes in four dimensions that contain only a single Killing vector field. These solutions, which we coin black resonators, link the superradiant instability of Kerr-AdS to the nonlinear weakly turbulent instability of AdS by connecting the onset of the superradiance instability to smooth, horizonless geometries called geons. Furthermore, they demonstrate non-uniqueness of Kerr-AdS by sharing asymptotic charges. Where black resonators coexist with Kerr-AdS, we find that the black resonators have higher entropy. Nevertheless, we …
Considerable effort has been dedicated to study the nonlinear instability of Anti-de Sitter (AdS) within spherical symmetry, but little is known about this nonlinear instability in the purely gravitational sector, where spherical symmetry is necessarily broken. In \cite{Bizon:2011gg} the onset of such nonlinear instability was associated with the existence of irremovable secular resonances at third order in perturbation theory. Furthermore, it was also conjectured in \cite{Bizon:2011gg} that certain very fine tuned initial data would not collapse. Such solutions, upon linearisation, correspond…
We investigate the existence and the stability of spherically symmetric thermal equilibrium states of the self-gravitating many-particle system which satisfies the Einstein-Vlasov equations with a negative cosmological constant. While a thermal equilibrium state of the self-gravitating particle system cannot have a finite mass without an artificial wall in the asymptotically flat case, in the asymptotically AdS case, the total mass can be finite without any artificial wall due to the AdS potential barrier. In this case, the typical size of the system is characterized by the AdS radius. The equ…
Here we have shown that asymptotically anti-de Sitter (AdS) black holes in the Einstein-Gauss-Bonnet (GB) theory are unstable under linear perturbations of spacetime in some region of parameters. This (eikonal) instability develops at high multipole numbers. We found the exact parametric regions of the eikonal instability and extended this consideration to asymptotically flat and de Sitter cases. The approach to the threshold of instability is driven by purely imaginary quasinormal modes, which are similar to those found recently in [5] for the higher curvature corrected black hole with the pl…
We show that for every asymptotically AdS solution compactified on a torus there is a corresponding Ricci-flat solution obtained by replacing the torus by a sphere, performing a Weyl rescaling of the metric and appropriately analytically continuing the dimension of the torus/sphere (as in generalized dimensional reduction). In particular, it maps Minkowski spacetime to AdS on a torus, the holographic stress energy tensor of AdS to the stress energy tensor due to a brane localized in the interior of spacetime and AdS black branes to (asymptotically flat) Schwarzschild black branes. Applying it …
It is now established that small Kerr-Anti-de Sitter (Kerr-AdS) black holes are unstable against scalar perturbations, via superradiant amplification mechanism. We show that small Kerr-AdS black holes are also unstable against gravitational perturbations and we compute the features of this instability. We also describe with great detail the evolution of this instability. In particular, we identify its endpoint state. It corresponds to a Kerr-AdS black hole whose boundary is an Einstein universe rotating with the light velocity. This black hole is expected to be slightly oblate and to co-exist …
In this review, we retrace the recent progress in the anti-de Sitter (AdS) instability problem. By instability we mean that for large classes of initial data, any perturbation of AdS space-time, however small, leads to the formation of a black hole. Since the seminal work of Bizoń and Rostworowski in 2011, many different kinds of numerical experiments were performed in asymptotically AdS space-times, unveiling a very intricate structure of the instability. In particular, many efforts were dedicated to the search of islands of stability, i.e.\ families of initial data that resist black hole for…
We study black holes in AdS-like spacetimes, with the horizon given by an arbitrary positive curvature Einstein metric. A criterion for classical instability of such black holes is found in the large and small black hole limits. Examples of large unstable black holes have a Böhm metric as the horizon. These, classically unstable, large black holes are locally thermodynamically stable. The gravitational instability has a dual description, for example by using the $AdS_7 \times S^4$ version of the AdS/CFT correspondence. The instability corresponds to a critical temperature of the dual thermal f…
We investigate instability of 4-dimensional Reissner-Nordström-anti-de Sitter (RN-AdS$_4$) black holes with various topologies by charged scalar field perturbations. We numerically find that the RN-AdS$_4$ black holes become unstable against the linear perturbations below a critical temperature. It is analytically shown that charge extraction from the black holes occurs during the unstable evolution. To explore the end state of the instability, we perturbatively construct static black hole solutions with the scalar hair near the critical temperature. It is numerically found that the entropy of…
Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied in [2]. In contrast with [2], we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symm…
We study the AdS/CFT correspondence with boundary conditions AdS_5 x S^5/Z_k, where the Z_k acts freely but breaks all supersymmetry. While there are closed string tachyons at small 't Hooft coupling, there are no tachyons at large coupling. Nevertheless, we show that there is a nonperturbative instability directly analogous to the decay of the Kaluza-Klein vacuum. We discuss the implications of this instability for the strongly coupled dual field theory, and compare with earlier studies of this theory at weak coupling.
We construct boson stars in global Anti de Sitter (AdS) space and study their stability. Linear perturbation results suggest that the ground state along with the first three excited state boson stars are stable. We evolve some of these solutions and study their nonlinear stability in light of recent work \cite{Bizon:2011gg} arguing that a weakly turbulent instability drives scalar perturbations of AdS to black hole formation. However evolutions suggest that boson stars are nonlinearly stable and immune to the instability for sufficiently small perturbation. Furthermore, these studies find othe…
Fermions scattering on a black hole background cannot develop an instability sourced by superradiance. However, in a global (or planar) AdS$_4$-Reissner-Nordström background fermions can violate the AdS$_2$ fermionic mass stability bound as measured by a near horizon observer at zero temperature. This suggests that AdS-Reissner-Nordström black holes might still be unstable to Dirac perturbations. Motivated by this observation we search for linear mode instabilities of Dirac fields in these backgrounds but find none. This is in contrast with the scalar field case, where a violation of the near-…
We study the thermodynamics and the phase structures of Reissner-Nordstrom and Born-Infeld black holes in AdS space by constructing ``off-shell'' free energies using thermodynamic quantities derived directly from the action. We then use these results to propose ``off-shell'' effective potentials for the respective boundary gauge theories. The saddle points of the potentials describe all the equilibrium phases of the gauge theories.
$AdS_5$ type IIb supergravity compactifications on five-dimensional Einstein manifolds ${\cal V}_5$ realize holographic duals to four-dimensional conformal field theories. Black holes in such geometries are dual to thermal states in these CFTs. When black holes become sufficiently small in (global) $AdS_5$, they are expected to suffer Gregory-Laflamme instability with respect to localization on ${\cal V}_5$. Previously, the instability was demonstrated for gravitational dual of ${\cal N}=4$ SYM, where ${\cal V}_5=S^5$. We extend stability analysis to arbitrary ${\cal V}_5$. We point out that t…
We construct the gauge field and graviton propagators in Euclidean AdS(d+1) space-time by two different methods. In the first method the gauge invariant Maxwell or linearized Ricci operator is applied directly to bitensor ansatze for the propagators which reflect their gauge structure. This leads to a rapid determination of the physical part of the propagators in terms of elementary functions. The second method is a more traditional approach using covariant gauge fixing which leads to a solution for both physical and gauge parts of the propagators. The gauge invariant parts agree in both metho…
We discuss dynamics of massive Klein-Gordon fields in two-dimensional Anti-de Sitter spacetimes ($AdS_2$), in particular conserved quantities and non-modal instability on the future Poincaré horizon called, respectively, the Aretakis constants and the Aretakis instability. We find out the geometrical meaning of the Aretakis constants and instability in a parallel-transported frame along a null geodesic, i.e., some components of the higher-order covariant derivatives of the field in the parallel-transported frame are constant or unbounded at the late time, respectively. Because $AdS_2$ is maxim…
We study gravitational perturbations of the Kerr-AdS_5 x S^5 spacetime with equal angular momenta. In this spacetime, we found the two kinds of classical instabilities, superradiant and Gregory-Laflamme instabilities. The superradiant instability is caused by the wave amplification via superradiance, and by wave reflection due to the potential barrier of the AdS spacetime. The Gregory-Laflamme instability appears in Kaluza-Klein modes of the internal space S^5 and breaks the symmetry SO(6). Taken into account these instabilities, the phase structure of Kerr-AdS_5 x S^5 spacetime is revealed. T…
We investigate the effects of an analytic boundary metric for smooth asymptotically anti-de Sitter gravitational solutions. The boundary dynamics is then completely determined by the initial data due to corner conditions that all smooth solutions must obey. We perturb a number of familiar static solutions and explore the boundary dynamics that results. We find evidence for a nonlinear asymptotic instability of the planar black hole in four and six dimensions. In four dimensions we find indications of at least exponential growth, while in six dimensions, it appears that a singularity may form i…
We explore a classical instability of spacetimes of dimension $D>4$. Firstly, we consider static solutions: generalised black holes and brane world metrics. The dangerous mode is a tensor mode on an Einstein base manifold of dimension $D-2$. A criterion for instability is found for the generalised Schwarzschild, AdS-Schwarzschild and topological black hole spacetimes in terms of the Lichnerowicz spectrum on the base manifold. Secondly, we consider perturbations in time-dependent solutions: Generalised dS and AdS. Thirdly we show that, subject to the usual limitations of a linear analysis, any …
Near-extreme Reissner-Nordstrom-anti-de Sitter black holes are unstable against the condensation of an uncharged scalar field with mass close to the Breitenlohner-Freedman bound. It is shown that a similar instability afflicts near-extreme large rotating AdS black holes, and near-extreme hyperbolic Schwarzschild-AdS black holes. The resulting nonlinear hairy black hole solutions are determined numerically. Some stability results for (possibly charged) scalar fields in black hole backgrounds are proved. For most of the extreme black holes we consider, these demonstrate stability if the ``effect…
It is well known that a weakly coupled U(N) gauge theory on a torus with sides of length L has extra light states with energies of order 1/NL. We show that a similar result holds for gauge theories on M/G where M is any compact Riemannian manifold and G is any freely acting discrete isometry group. As in the toroidal case, this is achieved by adding a suitable nontrivial flat connection. As one application, we consider the AdS/CFT correspondence on spacetimes asymptotic to AdS_5/G. By considering finite size effects at nonzero temperature, we show that consistency requires these extra light st…
Using a Hamiltonian approach, we introduce black hole entropy for Kerr-AdS spacetimes with torsion as the canonical charge on horizon. In spite of a completely different geometric setting with respect to GR, the resulting thermodynamic variables, energy, angular momentum and entropy, are shown to be proportional to the corresponding GR expressions. The validity of the first law is confirmed.
In this article, the behaviour of a charged and massive scalar field around a global monopole swallowed by a Reissner-Nordström-Anti-de Sitter (RN-AdS) black hole is investigated by considering the Klein-Gordon equation in this geometry. The superradiance phenomenon and instability behaviour of the black hole against charged scalar perturbations are studied for both an RN-AdS case and also for an RN black hole surrounded by a reflective mirror, i.e., the black hole bomb case. The effects of the monopole on these cases are discussed analytically and also with the help of several graphs in detai…
Using AdS/CFT prescription, we compute two point Yang-Mills correlator on a constant time slice for the Kasner background. Pushing the surface close to the initial singularity, we find, in some cases, the correlator does not develop pole. This is consistent with the observations made in a recent work. We further numerically calculate similar correlator where the bulk is a Kasner AdS soliton. We find that the qualitative behaviour of the correlator remains unchanged.
We study the stability of AdS black hole holes rotating in a single two plane for tensor-type gravitational perturbations in $D > 6$ space-time dimensions. First, by an analytic method, we show that there exists no unstable mode when the magnitude $a$ of the angular momentum is smaller than $r_h^2/R$ where $r_h$ is the horizon radius, and $R$ is the AdS curvature radius. Then, by numerical calculations of quasinormal modes, using the separability of the relevant perturbation equations, we show that an instability occurs for rapidly rotating black holes with $a>r_h^2/R$, although the growth rat…
Rotating small AdS black holes exhibit the superradiant instability to low-frequency scalar perturbations, which is amenable to a complete analytic description in four dimensions. In this paper, we extend this description to all higher dimensions, focusing on slowly rotating charged AdS black holes with a single angular momentum. We divide the spacetime of these black holes into the near-horizon and far regions and find solutions to the scalar wave equation in each of these regions. Next, we perform the matching of these solutions in the overlap between the regions, by employing the idea that …
We construct hairy black hole solutions that merge with the anti-de Sitter (AdS$_4$) Reissner-Nordström black hole at the onset of superradiance. These hairy black holes have, for a given mass and charge, higher entropy than the corresponding AdS$_4$-Reissner-Nordström black hole. Therefore, they are natural candidates for the endpoint of the charged superradiant instability. On the other hand, hairy black holes never dominate the canonical and grand-canonical ensembles. The zero-horizon radius of the hairy black holes is a soliton (i.e. a boson star under a gauge transformation). We construct…
The phenomenon of superradiance in the context of asymptotically global AdS spacetimes is investigated with particular accent on its effect on the stability of the systems under consideration. To this end, the concept of an asymptotically AdS spacetime is explained, together with its implications on the boundary conditions at $\mathcal{I}$, as well as the Newman-Penrose-Teukolsky formalism, whereby the Teukolsky master equation in a most general form for Kerr-AdS is given. Furthermore, work done in the cases of RN-AdS and Kerr-AdS is laid out in a concise manner, putting emphasis on the import…
We consider three-dimensional AdS gravity minimally coupled to a massless scalar field and study numerically the evolution of small smooth circularly symmetric perturbations of the $AdS_3$ spacetime. As in higher dimensions, for a large class of perturbations, we observe a turbulent cascade of energy to high frequencies which entails instability of $AdS_3$. However, in contrast to higher dimensions, the cascade cannot be terminated by black hole formation because small perturbations have energy below the black hole threshold. This situation appears to be challenging for the cosmic censor. Anal…
We present a numerical study of rotational dynamics in AdS$_5$ with equal angular momenta in the presence of a complex doublet scalar field. We determine that the endpoint of gravitational collapse is a Myers-Perry black hole for high energies and a hairy black hole for low energies. We investigate the timescale for collapse at low energies $E$, keeping the angular momenta $J\propto E$ in AdS length units. We find that the inclusion of angular momenta delays the collapse time, but retains a $t\sim1/E$ scaling. We perturb and evolve rotating boson stars, and find that boson stars near AdS appea…
We analyze the semiclassical stability of the Schwarzschild AdS black hole in the Euclidean partition function approach. We perform this computation in the large $D$ limit and focus on scalar perturbations. We obtain the equations for non-spherically symmetric scalar perturbations in a simple form. For a class of perturbations stability is demonstrated by the S-deformation method. For some other classes we rule out unstable modes of $\mathcal{O}(D^2)$. We also analyze the spherically symmetric perturbations and demonstrate the appearance of an unstable mode for small black holes in the large $…
We give strong numerical evidence that a self-interacting probe scalar field in AdS, with only a few modes turned on initially, will undergo fast thermalization only if it is above a certain energetic threshold. Below the threshold the energy stays close to constant in a few modes for a very long time instead of cascading quickly. This indicates the existance of a Strong Stochasticity Threshold (SST) in holography. The idea of SST is familiar from certain statistical mechanical systems, and we suggest that it exists also in AdS gravity. This would naturally reconcile the generic non-linear ins…
Inspired by the general relation between the boundary global symmetry and the bulk gauge symmetry in AdS/CFT, we reformulate the $d+1$ dimensional AdS gravity theory as a $SO(2,d)$ gauge theory. In this formalism, the pull back of the bulk equation of motion onto a co-dimension one hypersurface $Σ$ can be naturally related to the $SO(2,d)$ conservation law under a local energy scale in the dual CFT. The consistency of CFT requires that the $SO(2,d)$ covariant anomaly vanishes at arbitrary scale. After imposing a covariant area law as the renormalization condition, the vanishing of $SO(2,d)$ an…
We study thermodynamic instability of a class of $(n+1)$-dimensional charged dilaton black holes in the background of anti-de Sitter universe. We calculate the quasilocal mass of the AdS dilaton black hole through the use of the subtraction method of Brown and York. We find a Smarr-type formula and perform a stability analysis in the canonical ensemble and disclose the effect of the dilaton field on the thermal stability of the solutions. Our study shows that the solutions are thermally stable for small $α$, while for large $α$ the system has an unstable phase, where $α$ is a coupling constant…
Gravitational falling in AdS has two characteristic properties \cite{ohsin}: i) A thick shell becomes a thin shell. ii) Any shape become spherical. Such focusing character of AdS, for the collapse of dusts, leads to the rapid thermalization mechanism in strongly interacting system. For the collapse of a wave, it explains the cascade of energy to UV through repeated bounces, which has been extensively discussed in recent numerical works. Therefore the focusing is the physical mechanism of instability of AdS. Such sharp contrast between the dust and wave in collapse, together with the experiment…
Seiberg and Witten have discussed a specifically "stringy" kind of instability which arises in connection with "large" branes in asymptotically AdS spacetimes. It is easy to see that this instability actually arises in most five-dimensional asymptotically AdS black hole string spacetimes with non-trivial horizon topologies. We point out that this is a more serious problem than it may at first seem, for it cannot be resolved even by taking into account the effect of the branes on the geometry of spacetime. [It is ultimately due to the {\em topology} of spacetime, not its geometry.] Next, assumi…
