Asymptotically Anti-de Sitter Research Articles

Exactly solvable gravitating perfect fluid solitons in (2 + 1) dimensions

The Bogomolnyi-Prasad-Sommerfield (BPS) baby Skyrme model coupled to gravity is considered. We show that in an asymptotically flat space-time the model still possesses the BPS property, i.e., admits a BPS reduction to first order Bogomolnyi equations, which guarantees that the corresponding proper energy is a linear function of the topological charge. We also find the mass-radius relation as well as the maximal mass and radius. All these results are obtained in an analytical manner, which implies the complete solvability of this selfgravitating matter system.If a cosmological constant is added, then the BPS property is lost. In de Sitter (dS ) space-time both extremal and non-extremal solutions are found, where the former correspond to finite positive pressure solutions of the flat space-time model. For the asymptotic anti-de Sitter (AdS ) case, extremal solutions do not exist as there are no negative pressure BPS baby Skyrmions in flat space-time. Non-extremal solutions with AdS asymptotics do exist and may be constructed numerically. The impact of the negative cosmological constant on the mass-radius relation is studied. We also found two potentials for which exact multi-soliton solutions in the external AdS space can be obtained. Finally, we elaborate on the implications of these findings for certain three-dimensional models of holographic QCD.

Coherence effects in disordered geometries with a field-theory dual

We investigate the holographic dual of a probe scalar in an asymptotically Anti-de-Sitter (AdS) disordered background which is an exact solution of Einstein’s equations in three bulk dimensions. Unlike other approaches to model disorder in holography, we are able to explore quantum wave-like interference effects between an oscillating or random source and the geometry. In the weak-disorder limit, we compute analytically and numerically the one-point correlation function of the dual field theory for different choices of sources and backgrounds. The most interesting feature is the suppression of the one-point function in the presence of an oscillating source and weak random background. We have also computed analytically and numerically the two-point function in the weak disorder limit. We have found that, in general, the perturbative contribution induces an additional power-law decay whose exponent depends on the distribution of disorder. For certain choices of the gravity background, this contribution becomes dominant for large separations which indicates breaking of perturbation theory and the possible existence of a phase transition induced by disorder.

Evolution of the mean jet shape and dijet asymmetry distribution of an ensemble of holographic jets in strongly coupled plasma

Some of the most important experimentally accessible probes of the quark- gluon plasma (QGP) produced in heavy ion collisions come from the analysis of how the shape and energy of sprays of energetic particles produced within a cone with a specified opening angle (jets) in a hard scattering are modified by their passage through the strongly coupled, liquid, QGP. We model an ensemble of back-to-back dijets for the purpose of gaining a qualitative understanding of how the shapes of the individual jets and the asymmetry in the energy of the pairs of jets in the ensemble are modified by their passage through an expanding cooling droplet of strongly coupled plasma, in the model in a holographic gauge theory that is dual to a 4+1-dimensional black-hole spacetime that is asymptotically anti-de Sitter (AdS). We build our model by constructing an ensemble of strings in the dual gravitational description of the gauge theory. We model QCD jets in vacuum using strings whose endpoints are moving “downward” into the gravitational bulk spacetime with some fixed small angle, an angle that represents the opening angle (ratio of jet mass to jet energy) that the QCD jet would have in vacuum. Such strings must be moving through the gravitational bulk at (close to) the speed of light; they must be (close to) null. This condition does not specify the energy distribution along the string, meaning that it does not specify the shape of the jet being modeled. We study the dynamics of strings that are initially not null and show that strings with a wide range of initial conditions rapidly accelerate and become null and, as they do, develop a similar distribution of their energy density. We use this distribution of the energy density along the string, choose an ensemble of strings whose opening angles and energies are distributed as in perturbative QCD, and show that we can then fix one of the two model parameters such that the mean jet shape for the jets in the ensemble that we have built matches that measured in proton-proton collisions reasonably well. This is a novel way for hybridizing relevant inputs from perturbative QCD and a strongly coupled holographic gauge theory in the service of modeling jets in QGP. We send our ensemble of strings through an expanding cooling droplet of strongly coupled plasma, choosing the second model parameter so as to get a reasonable value for RAAjet, the suppression in the number of jets, and study how the mean jet shape and the dijet asymmetry are modified, comparing both to measurements from heavy ion collisions at the LHC.

A black hole with torsion in 5D Lovelock gravity

We analyze static spherically symmetric solutions of five dimensional (5D) Lovelock gravity in the first order formulation. In the Riemannian sector, when torsion vanishes, the Boulware–Deser black hole represents a unique static spherically symmetric black hole solution for the generic choice of the Lagrangian parameters. We show that a special choice of the Lagrangian parameters, different from the Lovelock Chern–Simons gravity, leads to the existence of a static black hole solution with torsion, the metric of which is asymptotically anti-de Sitter (AdS). We calculate the conserved charges and thermodynamical quantities of this black hole solution.

Gravitational collapse and Hawking-like radiation of a shell in AdS spacetime

In this paper, we study the collapse of a massive shell in 2+1 and 3+1 dimensional gravity with Anti-de Sitter asymptotics. Using the Gauss-Codazzi method, we derive gravitational equations of motion of the shell. We then use the functional Schrodinger formalism to calculate the spectrum of particles produced during the collapse. At the late time, radiation agrees very well with the standard Hawking results. In 3+1 dimensions, we reproduce the Hawking-Page transition. We then construct the density matrix of this collapsing system and analyze the information content in the emitted radiation. We find that the off-diagonal elements of the density matrix are very important in preserving the unitarity of the system.

Penrose inequality in anti–de Sitter space

For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti--de Sitter (AAdS) spacetimes, and show that the inequality holds for time asymmetric data in spherical symmetry. Our analysis is motivated by the constant-negative-spatial-curvature form of the AdS black hole metric.

Anti–de Sitter geon families

A detailed perturbative construction of globally regular, asymptotically anti-de Sitter (AdS) time-periodic solutions of Einstein's equations with a negative cosmological constant (AdS geons) is presented. Starting with the most general superposition of the $l=2$ even parity (scalar) eigenmodes of AdS at linear order, it is shown that at the fifth order in perturbation theory one obtains five one-parameter geon families, two of which have a helical Killing vector, one with axial symmetry, and two others without continuous symmetries. The details and some subtle aspects of the perturbative expansions are also presented.

Hawking radiation power equations for black holes

We derive the Hawking radiation power equations for black holes in asymptotically flat, asymptotically Anti-de Sitter (AdS) and asymptotically de Sitter (dS) black holes. This is done by using the greybody factor for these black holes. We observe that the radiation power equation for asymptotically flat black holes, corresponding to greybody factor at low frequency, depends on both the Hawking temperature and the horizon radius. However, for the greybody factors at asymptotic frequency, it only depends on the Hawking temperature. We also obtain the power equation for asymptotically AdS black holes both below and above the critical frequency. The radiation power equation for at asymptotic frequency is same for both Schwarzschild AdS and Reissner–Nordström AdS solutions and only depends on the Hawking temperature. We also discuss the power equation for asymptotically dS black holes at low frequency, for both even or odd dimensions.

Fixed mesh refinement in the characteristic formulation of general relativity

We implement a spatially fixed mesh refinement under spherical symmetry for the characteristic formulation of General Relativity. The Courant-Friedrich-Levy (CFL) condition lets us deploy an adaptive resolution in (retarded-like) time, even for the nonlinear regime. As test cases, we replicate the main features of the gravitational critical behavior and the spacetime structure at null infinity using the Bondi mass and the News function. Additionally, we obtain the global energy conservation for an extreme situation, i.e. in the threshold of the black hole formation. In principle, the calibrated code can be used in conjunction with an ADM 3+1 code to confirm the critical behavior recently reported in the gravitational collapse of a massless scalar field in an asymptotic anti-de Sitter spacetime. For the scenarios studied, the fixed mesh refinement offers improved runtime and results comparable to code without mesh refinement.

Quasinormal modes of a scalar field in the Einstein-Gauss-Bonnet-AdS black hole background: Perturbative and nonperturbative branches

It has recently been found that quasinormal modes of asymptotically anti-de Sitter (AdS) black holes in theories with higher curvature corrections may help to describe the regime of intermediate 't Hooft coupling in the dual field theory. Here, we consider quasinormal modes of a scalar field in the background of spherical Gauss--Bonnet--anti-de Sitter (AdS) black holes. In general, the eigenvalues of wave equations are found here numerically, but at a fixed Gauss-Bonnet constant $\alpha = R^2/2$ (where $R$ is the AdS radius), an exact solution of the scalar field equation has been obtained. Remarkably, the purely imaginary modes, which are usually appropriate only to some gravitational perturbations, were found here even for a test scalar field. These purely imaginary modes of the Einstein--Gauss--Bonnet theory do not have the Einsteinian limits, because their damping rates grow, when $\alpha$ is decreasing. Thus, these modes are nonperturbative in $\alpha$. The real oscillation frequencies of the perturbative branch are linearly related to their Schwarzschild-AdS limits $Re (\omega_{GB}) = Re (\omega_{SAdS}) (1+ K(D) (\alpha/R^2))$, where $D$ is the number of spacetime dimensions. Comparison of the analytical formula with the frequencies found by the shooting method allows us to test the latter. In addition, we found exact solutions to the master equations for gravitational perturbations at $\alpha=R^2/2$ and observed that for the scalar type of gravitational perturbations an eikonal instability develops.

Gravitational geons in asymptotically anti-de Sitter spacetimes

We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3 + 1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order ∼1/2 of the AdS length, and with deviations of the order of 50% compared to third order perturbative approaches. The consistency of our results with numerical resolution is carefully checked and we give extensive precision monitoring techniques. All global quantities, such as mass and angular momentum, are computed using two independent frameworks that agree with each other at the 0.1% level. We also provide strong evidence for the existence of ‘excited’ (i.e. with one radial node) geon solutions of Einstein equations in asymptotically AdS spacetimes by constructing them numerically.

New asymptotic Anti-de Sitter solution with a timelike extra dimension in 5D relativity

In 5D relativity, the usual 4D cosmological constant is determined by the extra dimension. If the extra dimension is spacelike, one can get a positive cosmological constant Λ and a 4D de Sitter (dS) space. In this paper we present that, if the extra dimension is timelike oppositely, the negative Λ will be emerged and the induced 4D space will be an asymptotic Anti-de Sitter (AdS). Under the minimum assumption, we solve the Kaluza–Klein equation RAB=0 in a canonical system and obtain the AdS solution in a general case. The result shows that an AdS space is induced naturally from a Kaluza–Klein manifold on a hypersurface (brane). The Lagrangian of test particle indicates the equation of motion can be geodesics if the 4D metric is independent of extra dimension. The causality is well respected because it is appropriately defined by a null higher dimensional interval. In this 5D relativity, the holographic principle can be used safely because the brane is asymptotic Euclidean AdS in the bulk. We also explore some possible holographic duality implications about the field/operator correspondence and the two-points correlation functions.

Eikonal instability of Gauss-Bonnet–(anti-)–de Sitter black holes

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 planar horizon. The found instability may indicate limits of holographic applicability of the GB-AdS backgrounds. Recently, through the analysis of critical behavior in AdS space-time in the presence of Gauss-Bonnet term, it was shown [19] that that, if the total energy content of the AdS space-time is small, then no black holes can be formed with mass less than some critical value. A similar mass gap was also found when considering collapse of mass shells in asymptotically flat Gauss-Bonnet theories [20]. The found instability of all sufficiently small Einstein-Gauss-Bonnet-AdS, -dS and asymptotically flat black holes may explain the existing mass gaps in their formation.

Black holes in quasi-topological gravity and conformal couplings

Lovelock theory of gravity provides a tractable model to investigate the effects of higher-curvature terms in the context of AdS/CFT. Yielding second order, ghost-free field equations, this theory represents a minimal setup in which higher-order gravitational couplings in asymptotically Anti-de Sitter (AdS) spaces, including black holes, can be solved analytically. This however has an obvious limitation as in dimensions lower than seven, the contribution from cubic or higher curvature terms is merely topological. Therefore, in order to go beyond quadratic order and study higher terms in AdS5 analytically, one is compelled to look for other toy models. One such model is the so-called quasi-topological gravity, which, despite being a higher-derivative theory, provides a tractable setup with R3 and R4 terms. In this paper, we investigate AdS5 black holes in quasi-topological gravity. We consider the theory conformally coupled to matter and in presence of Abelian gauge fields. We show that charged black holes in AdS5 which, in addition, exhibit a backreaction of the matter fields on the geometry can be found explicitly in this theory. These solutions generalize the black hole solution of quasi-topological gravity and exist in a region of the parameter spaces consistent with the constraints coming from causality and other consistency conditions. They have finite conserved charges and exhibit non-trivial thermodynamical properties.

Heavy fields and gravity

We study the effects of heavy fields on 4D spacetimes with flat, de Sitter and anti-de Sitter asymptotics. At low energies, matter generates specific, calculable higher derivative corrections to the GR action which perturbatively alter the Schwarzschild-(A)dS family of solutions. The effects of massive scalars, Dirac spinors and gauge fields are each considered. The six-derivative operators they produce, such as ∼ R3 terms, generate the leading corrections. The induced changes to horizon radii, Hawking temperatures and entropies are found. Modifications to the energy of large AdS black holes are derived by imposing the first law. An explicit demonstration of the replica trick is provided, as it is used to derive black hole and cosmological horizon entropies. Considering entropy bounds, it’s found that scalars and fermions increase the entropy one can store inside a region bounded by a sphere of fixed size, but vectors lead to a decrease, oddly. We also demonstrate, however, that many of the corrections fall below the resolving power of the effective field theory and are therefore untrustworthy. Defining properties of black holes, such as the horizon area and Hawking temperature, prove to be remarkably robust against higher derivative gravitational corrections.

Thermodynamics of (2+1)-dimensional charged black holes with power-law Maxwell field

In this work, the three-dimensional nonlinearly charged black holes have been considered with a power-law modified electromagnetic theory. The black hole solutions to Einstein's three-dimensional field equations with a negative cosmological constant have been constructed in the presence of power-law nonlinear electrodynamics. Through the physical and mathematical interpretation of the solutions, a new class of asymptotically anti--de Sitter (AdS) black hole solutions has been introduced. The area law, surface gravity, and Gauss's law are utilized to obtain the entropy, temperature, and electric charge of the new AdS black holes, respectively. The quasilocal mass of the solutions has been calculated based on the counterterm method. A Smarr-type formula for the mass as a function of entropy and charge has been obtained. It has been shown that the thermodynamical quantities satisfy the first law of thermodynamics for the new AdS black holes. Also, it has been found that in order for the Smarr mass formula to be compatible with the first law of black hole thermodynamics, the cosmological parameter $\mathrm{\ensuremath{\Lambda}}$ should be treated as a thermodynamical variable and the generalized first law of thermodynamics has been introduced. Through the canonical ensemble method, the black hole remnant or phase transitions have been investigated regarding the black hole heat capacity. It has been found that the AdS black hole solutions we just obtained are thermodynamically stable.

AdS and dS black hole solutions in analogue gravity: The relativistic and nonrelativistic cases

We show that Schwarzschild black hole solutions in asymptotically Anti-de Sitter (AdS) and de Sitter (dS) spaces may, up to a conformal factor, be reproduced in the framework of analogue gravity. The aforementioned derivation is performed using relativistic and non-relativistic Bose-Einstein condensates. In addition, we demonstrate that the (2+1) planar AdS black hole can be mapped into the non-relativistic acoustic metric. Given that AdS black holes are extensively employed in the gauge/gravity duality, we then comment on the possibility to study the AdS/CFT correspondence and gravity/fluid duality from an analogue gravity perspective.

Black hole thermodynamics, conformal couplings, and R 2 terms

Lovelock theory provides a tractable model of higher-curvature gravity in which several questions can be studied analytically. This is the reason why, in the last years, this theory has become the favorite arena to study the effects of higher-curvature terms in the context of AdS/CFT correspondence. Lovelock theory also admits extensions that permit to accommodate matter coupled to gravity in a non-minimal way. In this setup, problems such as the backreaction of matter on the black hole geometry can also be solved exactly. In this paper, we study the thermodynamics of black holes in theories of gravity of this type, which include both higher-curvature terms, U(1) gauge fields, and conformal couplings with matter fields in D dimensions. These charged black hole solutions exhibit a backreacting scalar field configuration that is regular everywhere outside and on the horizon, and may exist both in asymptotically flat and asymptotically Anti-de Sitter (AdS) spaces. We work out explicitly the boundary action for this theory, which renders the variational problem well-posed and suffices to regularize the Euclidean action in AdS. We also discuss several interrelated properties of the theory, such as its duality symmetry under field redefinition and how it acts on black holes and gravitational wave solutions.

Phase transitions of black holes in massive gravity

In this paper, we have studied thermodynamics of a black hole in massive gravity in the canonical ensemble. The massive gravity theory in consideration here has a massive graviton due to Lorentz symmetry breaking. The black hole studied here has a scalar charge due to the massive graviton and is asymptotically anti-de Sitter (AdS). We have computed various thermodynamical quantities such as temperature, specific heat and free energy. Both the local and global stability of the black hole are studied by observing the behavior of the specific heat and the free energy. We have observed that there is a first-order phase transition between small (SBH) and large black hole (LBH) for a certain range of the scalar charge. This phase transition is similar to the liquid/gas phase transition at constant temperature for a van der Waals fluid. The coexistence curves for the SBH and LBH branches are also discussed in detail.

Self-similar equilibration of strongly interacting systems from holography

We study the equilibration of a class of far-from-equilibrium strongly interacting systems using gauge-gravity duality. The systems we analyze are $2+1$ dimensional and have a four-dimensional gravitational dual. A prototype example of a system we analyze is the equilibration of a two-dimensional fluid which is translational invariant in one direction and is attached to two different heat baths with different temperatures at infinity in the other direction. We realize such setup in gauge-gravity duality by joining two semi-infinite asymptotically anti-de Sitter (AdS) black branes of different temperatures, which subsequently evolve towards equilibrium by emitting gravitational radiation towards the boundary of AdS. At sufficiently late times the solution converges to a similarity solution, which is only sensitive to the left and right equilibrium states and not to the details of the initial conditions. This attractor solution not only incorporates the growing region of equilibrated plasma but also the outwardly propagating transition regions, and can be constructed by solving a single ordinary differential equation.