Alex S. Miranda

Geodesic stability, Lyapunov exponents, and quasinormal modes

Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d ≥ 6.

Black-hole quasinormal modes and scalar glueballs in a finite-temperature AdS/QCD model

We use the holographic AdS/QCD soft-wall model to investigate the spectrum of scalar glueballs in a finite temperature plasma. In this model, glueballs are described by a massless scalar field in an AdS5 black hole with a dilaton soft-wall background. Using AdS/CFT prescriptions, we compute the boundary retarded Greens function. The corresponding thermal spectral function shows quasiparticle peaks at low temperatures. We also compute the quasinormal modes of the scalar field in the soft-wall black hole geometry. The temperature and momentum dependences of these modes are analyzed. The positions and widths of the peaks of the spectral function are related to the frequencies of the quasinormal modes. Our numerical results are found employing the power series method and the computation of Breit-Wigner resonances.

Quasinormal modes of black holes in anti-de Sitter space: A numerical study of the eikonal limit

Using series solutions and time-domain evolutions, we probe the eikonal limit of the gravitational and scalar-field quasinormal modes of large black holes and black branes in anti-de Sitter backgrounds. These results are particularly relevant for the AdS/CFT correspondence, since the eikonal regime is characterized by the existence of long-lived modes which (presumably) dominate the decay time scale of the perturbations. We confirm all the main qualitative features of these slowly damped modes as predicted by Festuccia and Liu [G. Festuccia and H. Liu, arXiv:0811.1033.] for the scalar-field (tensor-type gravitational) fluctuations. However, quantitatively we find dimensional-dependent correction factors. We also investigate the dependence of the quasinormal mode frequencies on the horizon radius of the black hole (brane) and the angular momentum (wave number) of vector- and scalar-type gravitational perturbations.

Gravitational quasinormal modes of AdS black branes in d spacetime dimensions

The AdS/CFT duality has established a mapping between quantities in the bulk AdS black-hole physics and observables in a boundary finite-temperature field theory. Such a relationship appears to be valid for an arbitrary number of spacetime dimensions, extrapolating the original formulations of Maldacenas correspondence. In the same sense properties like the hydrodynamic behavior of AdS black-hole fluctuations have been proved to be universal. We investigate in this work the complete quasinormal spectra of gravitational perturbations of d-dimensional plane-symmetric AdS black holes (black branes). Holographically the frequencies of the quasinormal modes correspond to the poles of two-point correlation functions of the field-theory stress-energy tensor. The important issue of the correct boundary condition to be imposed on the gauge-invariant perturbation fields at the AdS boundary is studied and elucidated in a fully d-dimensional context. We obtain the dispersion relations of the first few modes in the low-, intermediate- and high-wavenumber regimes. The sound-wave (shear-mode) behavior of scalar (vector)-type low-frequency quasinormal mode is analytically and numerically confirmed. These results are found employing both a power series method and a direct numerical integration scheme.

Vector meson quasinormal modes in a finite-temperature AdS/QCD model

A bstractWe study the spectrum of vector mesons in a finite temperature plasma. The plasma is holographically described by a black hole AdS/QCD model. We compute the boundary retarded Green’s functions using AdS/CFT prescriptions. The corresponding thermal spectral functions show quasiparticle peaks at low temperatures. Then we calculate the quasinormal modes of vector mesons in the soft-wall black hole geometry and analyse their temperature and momentum dependences.

GRAVITATIONAL PERTURBATIONS AND QUASINORMAL MODES OF BLACK HOLES WITH NON-SPHERICAL TOPOLOGY

In the present work we investigate the physical interpretation of gravitational perturbations of static asymptotically anti-de Sitter black holes with non-spherical topology. For zero wavenumber modes, the axial perturbations yield only small rotations on the system, while the polar perturbations lead to a change in the mass and may also produce gravitational waves. Additionally, it is verified that perturbations with any nonzero wavenumber are able to produce gravitational waves in these space–times. On the basis of these results, the quasinormal frequencies corresponding to polar perturbation modes with null wavenumber are calculated and briefly analyzed.

Electromagnetic quasinormal modes of rotating black strings and the AdS/CFT correspondence

A bstractWe investigate the quasinormal spectrum of electromagnetic perturbations of rotating black strings. Among the solutions of Einstein equations in the presence of a negative cosmological constant there are asymptotically anti-de Sitter (AdS) black holes whose horizons have the topology of a cylinder. The stationary version of these AdS black holes represents rotating black strings. The conformal field theory (CFT) dual of a black string lives in a Minkowski space with a compact dimension. On the basis of the AdS/CFT duality, we interpret a CFT plasma moving with respect to the preferred rest frame introduced by the topology as the holographic dual to a rotating black string. We explore the consequences of this correspondence by investigating the electromagnetic perturbations of a black string for different rotation parameter values. As usual the electromagnetic quasinormal modes (QNM) correspond to the poles of retarded Green’s functions of R-symmetry currents in the boundary field theory. The hydrodynamic regime of the QNM dispersion relations are analytically studied. Finally, we investigate numerically the effect of rotation on all the family of black-string electromagnetic quasinormal modes. We interpret these results from the CFT perspective and notice the emergence of effects like Doppler shift of the frequencies and dilation of the thermalization times.

Effective holographic models for QCD: glueball spectrum and trace anomaly

We investigate effective holographic models for QCD arising from five dimensional Dilaton-Gravity. The models are characterized by a dilaton with a mass term in the UV, dual to a CFT deformation by a relevant operator, and quadratic in the IR. The UV constraint leads to the explicit breaking of conformal symmetry whereas the IR constraint guarantees linear confinement. We propose semi-analytic interpolations between the UV and the IR and obtain a spectrum for scalar and tensor glueballs consistent with lattice QCD data. We use the glueball spectrum as a physical constraint to find the evolution of the model parameters as the mass term goes to zero. Finally, we reproduce the universal result for the trace anomaly of deformed CFTs and propose a dictionary between this result and the QCD trace anomaly. A nontrivial consequence of this dictionary is the emergence of a

Glueballs at finite temperature from AdS/QCD

\beta

Separable wave equations for gravitoelectromagnetic perturbations of rotating charged black strings

function similar to the two-loop perturbative QCD result.