Pure Anti-de Sitter Research Articles

Holographic Characterisation of Locally Anti-de Sitter Spacetimes

It is shown that an (n+1)-dimensional asymptotically anti-de Sitter solution of the Einstein-vacuum equations is locally isometric to pure anti-de Sitter spacetime near a region of the conformal boundary if and only if the boundary metric is conformally flat and (for n ne 4) the boundary stress–energy tensor vanishes, subject to (i) sufficient (finite) regularity in the metric and (ii) the satisfaction of a conformally invariant geometric criterion on the boundary region. A key tool in the proof is the Carleman estimate of Chatzikaleas and Shao (Commun Math Phys, 2022)—a generalisation of previous work by the author with McGill and Shao in (Class Quant Gravity 38(5), 2020)—which is applied to prove a unique continuation result for the Weyl curvature at the conformal boundary given vanishing to sufficiently high order over the boundary region.

Maxwell quasinormal modes on a global monopole Schwarzschild-anti-de Sitter black hole with Robin boundary conditions

We generalize our previous studies on the Maxwell quasinormal modes around Schwarzschild-anti-de-Sitter black holes with Robin type vanishing energy flux boundary conditions, by adding a global monopole on the background. We first formulate the Maxwell equations both in the Regge–Wheeler–Zerilli and in the Teukolsky formalisms and derive, based on the vanishing energy flux principle, two boundary conditions in each formalism. The Maxwell equations are then solved analytically in pure anti-de Sitter spacetimes with a global monopole, and two different normal modes are obtained due to the existence of the monopole parameter. In the small black hole and low frequency approximations, the Maxwell quasinormal modes are solved perturbatively on top of normal modes by using an asymptotic matching method, while beyond the aforementioned approximation, the Maxwell quasinormal modes are obtained numerically. We analyze the Maxwell quasinormal spectrum by varying the angular momentum quantum number ell , the overtone number N, and in particular, the monopole parameter 8pi eta ^2. We show explicitly, through calculating quasinormal frequencies with both boundary conditions, that the global monopole produces the repulsive force.

Inhomogeneous Jacobi equation for minimal surfaces and perturbative change in holographic entanglement entropy

The change in Holographic entanglement entropy (HEE) for small fluctuations about pure anti De Sitter (AdS) is obtained by a perturbative expansion of the area functional in terms of the change in the bulk metric and the embedded extremal surface. However, it is known that change in the embedding appears in second order or higher. It was shown that these changes in the embedding can be calculated in the $2+1$ dimensional case by solving a generalized geodesic deviation equation. We generalize this result to arbitrary dimensions by deriving an inhomogeneous form of the Jacobi equation for minimal surfaces. The solutions of this equation map a minimal surface in a given space time to a minimal surface in a space time which is a perturbation over the initial space time. Using this we perturbatively calculate the changes in HEE upto second order for boosted black brane like perturbations over $AdS 4$ .

A defect in holographic interpretations of tensor networks

We initiate the study of how tensor networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain tensors require updating. On the other hand, even identical tensors can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating tensor updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS3-Janus geometries.

Vacuum densities for a brane intersecting the AdS boundary

We investigate the Wightman function, the bulk-to-boundary propagator, the mean field squared, and the vacuum expectation values of energy-momentum tensor for a scalar field in anti--de Sitter (AdS) spacetime, in the presence of a brane perpendicular to the AdS boundary. On the brane the field operator obeys the Robin boundary condition. The vacuum expectation values are decomposed into the boundary-free AdS and brane-induced contributions. In this way, for points away from the brane, the renormalization is reduced to the one in pure AdS spacetime. It is shown that at proper distances from the brane larger than the AdS curvature radius the brane-induced expectation values decay as power law for both massless and massive scalars. This behavior is in contrast to that for a plane boundary in Minkowski spacetime, with an exponential decay for massive fields. For Robin boundary conditions different from Dirichlet and Neumann ones, the brane-induced part in the energy density is positive near the brane and negative at large distances. For the Dirichlet/Neumann boundary condition the corresponding energy density is negative/positive everywhere. We show that, for a fixed value of the proper distance from the brane, near the AdS boundary, the Neumann boundary condition is an ``attractor'' in the general class of Robin boundary conditions, whereas the Dirichlet boundary condition is an attractor near the horizon.

Fermionic vacuum polarization by a cosmic string in anti-de Sitter spacetime

In this paper, we investigate the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy–momentum tensor, associated with a massive fermionic field, induced by the presence of a cosmic string in the anti-de Sitter (AdS) spacetime. In order to develop this analysis we construct the complete set of normalized eigenfunctions in the corresponding spacetime. We consider a special case of boundary conditions on the AdS boundary, when the MIT bag boundary condition is imposed on the field operator at a finite distance from the boundary, which is then taken to zero. The FC and the VEV of the energy–momentum tensor are decomposed into the pure AdS and string-induced parts. Because the analysis of one-loop quantum effects in the AdS spacetime has been developed in the literature, here we are mainly interested to investigate the influence of the cosmic string on the VEVs. The string-induced part in the VEV of the energy–momentum tensor is diagonal and the axial and radial stresses are equal to the energy density. For points near the string, the effects of the curvature are subdominant and to leading order, the VEVs coincide with the corresponding VEVs for the cosmic string in the Minkowski bulk. At large proper distances from the string, the decay of the VEVs show a power-law dependence of the distance for both massless and massive fields. This is in contrast to the case of the Minkowski bulk where, for a massive field, the string-induced parts decay exponentially.

Kinematical and dynamical aspects of higher-spin bound-state equations in holographic QCD

In this paper we derive holographic wave equations for hadrons with arbitrary spin starting from an effective action in a higher-dimensional space asymptotic to anti--de Sitter (AdS) space. Our procedure takes advantage of the local tangent frame, and it applies to all spins, including half-integer spins. An essential element is the mapping of the higher-dimensional equations of motion to the light-front Hamiltonian, thus allowing a clear distinction between the kinematical and dynamical aspects of the holographic approach to hadron physics. Accordingly, the nontrivial geometry of pure AdS space encodes the kinematics, and the additional deformations of AdS space encode the dynamics, including confinement. It thus becomes possible to identify the features of holographic QCD, which are independent of the specific mechanisms of conformal symmetry breaking. In particular, we account for some aspects of the striking similarities and differences observed in the systematics of the meson and baryon spectra.

Scalar collapse in AdS spacetimes

Recently, studies of the gravitational collapse of a scalar field within spherically symmetric anti--de Sitter (AdS) spacetimes presented by Bizon and Rostroworoski [Phys. Rev. Lett. 107, 031102 (2011)], Jalmuzna et al. [Phys. Rev. D 84, 085021 (2011).] showed an instability of pure AdS to black hole formation. In particular, the work showed that arbitrarily small initial configurations of a scalar field evolved through some number of reflections off the AdS boundary until a black hole forms. We consider this same system, extended to include a complex scalar field, and reproduce this phenomena. We present tests of our numerical code that demonstrate convergence and consistency. We study the properties of the evolution as the scalar pulse becomes more compact by examining the asymptotic behavior of the scalar field, an observable in the corresponding boundary conformal field theory. We demonstrate that such black hole formation occurs even when one places a reflecting boundary at finite radius, indicating that the sharpening is a property of gravity in a bounded domain and not of AdS itself. We examine how the initial energy is transferred to higher frequencies---which leads to black hole formation---and uncover interesting features of this transfer.

Vacuum polarization induced by a cosmic string in anti-de Sitter spacetime

In this paper, we investigate the vacuum expectation values (VEVs) of the field squared and the energy–momentum tensor associated with a massive scalar quantum field induced by a generalized cosmic string in D-dimensional anti-de Sitter (AdS) spacetime. In order to develop this analysis we evaluate the corresponding Wightman function. As we shall observe, this function is expressed as the sum of two terms: the first one corresponds to the Wightman function in pure AdS bulk and the second one is induced by the presence of the string. The second contribution is finite at the coincidence limit and is used to provide closed expressions for the parts in the VEVs of the field squared and the energy–momentum tensor induced by the presence of the string. Because the analysis of vacuum polarization effects in pure AdS spacetime has been developed in the literature, here we are mainly interested in the investigation of string-induced effects. We show that the curvature of the background spacetime has an essential influence on the VEVs at distances larger than the curvature radius. In particular, at large distances the decay of the string-induced VEVs is power law for both massless and massive fields. The string-induced parts vanish on the AdS boundary and they dominate the pure AdS part for points near the AdS horizon.

Greybody Factors for d-Dimensional Black Holes

Gravitational greybody factors are analytically computed for static, spherically symmetric black holes in d-dimensions, including black holes with charge and in the presence of a cosmological constant (where a proper definition of greybody factors for both asymptotically de Sitter and Anti-de Sitter spacetimes is provided). This calculation includes both the low-energy case—where the frequency of the scattered wave is small and real—and the asymptotic case—where the frequency of the scattered wave is very large along the imaginary axis—addressing gravitational perturbations as described by the Ishibashi-Kodama master equations, and yielding full transmission and reflection scattering coefficients for all considered spacetime geometries. At low frequencies a general method is developed, which can be employed for all three types of spacetime asymptotics, and which is independent of the details of the black hole. For asymptotically de Sitter black holes the greybody factor is different for even or odd spacetime dimension, and proportional to the ratio of the areas of the event and cosmological horizons. For asymptotically Anti-de Sitter black holes the greybody factor has a rich structure in which there are several critical frequencies where it equals either one (pure transmission) or zero (pure reflection, with these frequencies corresponding to the normal modes of pure Anti-de Sitter spacetime). At asymptotic frequencies the computation of the greybody factor uses a technique inspired by monodromy matching, and some universality is hidden in the transmission and reflection coefficients. For either charged or asymptotically de Sitter black holes the greybody factors are given by non-trivial functions, while for asymptotically Anti-de Sitter black holes the greybody factor precisely equals one (corresponding to pure blackbody emission).

Asymptotically anti-de Sitter spacetimes and conserved quantities in higher curvature gravitational theories

We consider $n$-dimensional asymptotically anti-de Sitter spacetimes in higher curvature gravitational theories with $n\ensuremath{\ge}4$, by employing the conformal completion technique. We first argue that a condition on the Ricci tensor should be supplemented to define an asymptotically anti-de Sitter spacetime in higher curvature gravitational theories and propose an alternative definition of an asymptotically anti-de Sitter spacetime. Based on that definition, we then derive a conservation law of the gravitational field and construct conserved quantities in two classes of higher curvature gravitational theories. We also show that these conserved quantities satisfy a balance equation in the same sense as in Einstein gravity and that they reproduce the results derived elsewhere. These conserved quantities are shown to be expressed as an integral of the electric part of the Weyl tensor alone and hence they vanish identically in the pure anti-de Sitter spacetime as in the case of Einstein gravity.

Phases of R-charged black holes, spinning branes and strongly coupled gauge theories

We study the thermodynamic stability of charged black holes in gauged supergravity theories in D=5, D=4 and D=7. We find explicitly the location of the Hawking-Page phase transition between charged black holes and the pure anti-de Sitter space-time, both in the grand-canonical ensemble, where electric potentials are held fixed, and in the canonical ensemble, where total charges are held fixed. We also find the explicit local thermodynamic stability constraints for black holes with one non-zero charge. In the grand-canonical ensemble, there is in general a region of phase space where neither the anti-de Sitter space-time is dynamically preferred, nor are the charged black holes thermodynamically stable. But in the canonical ensemble, anti-de Sitter space-time is always dynamically preferred in the domain where black holes are unstable. We demonstrate the equivalence of large R-charged black holes in D=5, D=4 and D=7 with spinning near-extreme D3-, M2- and M5-branes, respectively. The mass, the charges and the entropy of such black holes can be mapped into the energy above extremality, the angular momenta and the entropy of the corresponding branes. We also note a peculiar numerological sense in which the grand-canonical stability constraints for large charge black holes in D=4 and D=7 are dual, and in which the D=5 constraints are self-dual.

Geometric Models of the Quantum Relativistic Rotating Oscillator

A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual isotropic harmonic oscillator in the nonrelativistic limit, even though their relativistic behavior is different. As in the case of the (1+1) models,1 these will have even countable energy spectra or mixed ones, with a finite discrete sequence and a continuous part. In addition, all these spectra, except that of the pure anti-de Sitter model, will have a fine-structure, given by a rotator-like term.