The electromagnetic and gravitational quasinormal spectra of (3 + 1)dimensional plane-symmetric anti-de Sitter black holes are analyzed in the context of the AdS/CFT correspondence. According to such a correspondence, the electromagnetic and gravitational quasinormal frequencies of these black holes are associated respectively to the poles of retarded correlation functions of R-symmetry currents and stress-energy tensor in the holographically dual conformal field theory: the (2+1)-dimensional N = 8 super-Yang-Mills theory. The connection between AdS black holes and the corresponding field theory is used to unambiguously fix the boundary conditions that enter the proper definition of quasinormal modes. Such a procedure also helps one to decide, among the various different possibilities, what are the appropriate gauge-invariant quantities one should use in order to correctly describe the electromagnetic and gravitational blackhole perturbations. These choices imply in different dispersion relations for the quasinormal modes when compared to some of the results in the literature. In particular, the long-distance, low-frequency limit of dispersion relations presents the characteristic hydrodynamic behavior of a conformal field theory with the presence of diffusion, shear, and sound wave modes. There is also a family of purely damped electromagnetic modes which tend to the bosonic Matsubara frequencies in the long-wavelength regime.

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 Maldacena's 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.

Using series solutions and time-domain evolutions, we probe the eikonal limit of the gravitational and scalarfield 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 timescale of the perturbations. We confirm all the main qualitative features of these slowly-damped modes as predicted by Festuccia and Liu [14] for the scalarfield (tensor-type gravitational) fluctuations. However, quantitatively we find dimensional-dependent correction factors. We also investigate the dependence of the QNM frequencies on the horizon radius of the black hole (brane) and the angular momentum (wavenumber) of vector-and scalar-type gravitational perturbations.

A certain identification of points in a planar Schwarzschild-anti de Sitter (AdS) black hole generates a four-dimensional static black string. In turn, a rotating black string can be obtained from a static one by means of a local boost along the compact direction. On the basis of the gauge/gravity duality, these black strings are dual to rotating thermal states of a strongly interacting conformal field theory (CFT) that lives on a cylinder. In this work, we obtain the complete quasinormal mode (QNM) spectrum of the gravitational perturbations of rotating black strings. Analytic solutions for the dispersion relations are found in the hydrodynamic limit, characterized by fluctuations with wavenumber and frequency much smaller than the Hawking temperature of the string (or the temperature of the CFT in the dual description). We obtain these dispersion relations both by studying the gravitational perturbations of rotating black strings and by investigating relativistic wave vectors in a moving fluid living on the boundary of the AdS spacetime. Relativistic effects like the Doppler shift of the frequencies, wavelength contraction, and dilation of the thermalization time are shown explicitly in such a regime. The numerical solutions for the fundamental QNMs show a crossover (a transition) from a hydrodynamic-like behavior to a linear relativistic scaling for large wavenumbers. Additionally, we find a new family of QNMs which are purely damped in the zero wavenumber limit and that does not follow as a continuation of QNMs of the static black string, but that appears to be closely related to the algebraically special perturbation modes. I. INTRODUCTIONSince its advent in the late 1990's, the celebrated antide Sitter/conformal field theory (AdS/CFT) correspondence [1-4] has been extended and applied to different areas of physics. Such developments have lead to what is now known as the AdS/QCD [5][6][7][8], the AdS/condensed matter [9][10][11], and the fluid/gravity [12][13][14] correspondences. Over the last two decades, the AdS/CFT duality has allowed the study of properties of strongly coupled systems in a n-dimensional flat spacetime by mapping them to a weakly coupled gravitational theory in an asymptotically AdS n+1 spacetime. In applications to particle physics, top-down and bottom-up models were used to study, among other things, the mass spectrum, the correlation functions, and the deep inelastic scattering of glueballs, vector and scalar mesons [15][16][17][18][19][20][21][22][23]. Some phenomena in condensed matter, such as the hightemperature superconductivity [24][25][26], the classical and quantum Hall effects [27][28][29][30][31][32] and the (non-)Fermi liquid behavior of certain materials [33][34][35], were also object of study in the literature. In relation to plasma physics, the fluid/gravity correspondence establishes a one-to-one

Abstract.Rotating charged black strings are exact solutions of four-dimensional EinsteinMaxwell equations with a negative cosmological constant and a non-trivial spacetime topology. According to the AdS/CFT correspondence, these black strings are dual to rotating thermal states of a strongly interacting quantum field theory with nonzero chemical potential that lives in a cylinder. The dynamics of linear fluctuations in the dual field theory can be studied from the perturbation equations for classical fields in a black-string spacetime. With this motivation in mind, we develop here a completely gauge and tetrad invariant perturbation approach to deal with the gravitoelectromagnetic fluctuations of rotating charged black strings in the presence of sources. As usual, for any charged black hole, a perturbation in the background electromagnetic field induces a metric perturbation and vice versa. In spite of this coupling and the non-vanishing angular momentum, we show that linearization of equations of the Newman-Penrose formalism leads to four separated second-order complex equations for suitable combinations of the spin coefficients, the Weyl and the Maxwell scalars. Then, we generalize the Chandrasekhar transformation theory by the inclusion of sources and apply it to reduce the perturbation problem to four decoupled inhomogeneous wave equations -a pair for each sector of perturbations. The radial part of such wave equations can be put into Schrödinger-like forms after Fourier transforming them with respect to time. We find that the resulting effective potentials form two pairs of supersymmetric partner potentials and, as a consequence, the fundamental variables of one perturbation sector are related to the variables of the other sector. The relevance of such a symmetry in connection to the AdS/CFT correspondence is discussed, and future applications of the pertubation theory developed here are outlined.