Gravitational quasinormal modes of AdS black branes indspacetime dimensions

Abstract

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.

Quasinormal modes of black holes: From astrophysics to string theory

“…In addition, quasinormal ringing was studied for the four-dimensional Kerr-AdS black hole 163 and planar AdS black holes in four and higher dimensions [164][165][166] . An alternative, perturbative approach for finding quasinormal modes was developed in 167,168 for asymptotically flat and AdS black holes.…”

Perturbations of blackp-branes

“…One very recent work complement our analysis presented here [16]. But although the presented work and [16] are complementary and relevant in terms of the AdS/CFT correspon-dence, they treat different geometries and focus on different issues.…”

“…But although the presented work and [16] are complementary and relevant in terms of the AdS/CFT correspon-dence, they treat different geometries and focus on different issues. The results presented in this paper address directly the role of the brane structure (in the sense presented in [2,4]) on the gravitation-field theory duality, specifically searching for possible instabilities.…”

New results on quasinormal modes of anti-de Sitter black holes

“…The fundamental equations for the vectorial and scalar sectors can be see in [9]. An important characteristic of classical field evolutions on asymptotically AdS spacetimes is the variety of choices for the boundary conditions at spatial infinity.…”

“…There is only one exception: for scalar-type perturbations in four spacetime dimensions, the boundary condition that leads to QNM frequencies corresponding to poles of retarded correlation functions is of Robin type. However, when we consider the variable Z p the Dirichlet condition at spatial infinity leads to QNM frequencies corresponding to poles of retarded correlation functions for all cases [9,10].…”