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

Abstract

In this work we study the quasinormal spectra of gravitational perturbations of d-dimensional plane-symmetric AdS black holes in the context of the AdS/CFT correspondence. The perturbation equations are written for two different gauge-invariant variables: in the first the variables are chosen in such a way to put the radial part of the fundamental equations into a Schrödinger-like form; in the second we have a new set of fundamental variables where the imposition of Dirichlet boundary conditions at infinity leads exactly to the quasinormal frequencies associated to black hole here studied. The AdS/CFT correspondence helps one to find an appropriate condition to be applied to each set of variables at the AdS space boundary in order to produce identical QNM spectra for a given sector of perturbations, and more, that the quasinormal modes will correspond to the poles of the stress-energy tensor correlators in the dual field theory. We investigate analytically the quasinormal spectrum for small wavenumbers, large frequencies, and large number of spacetime dimensions. Using series solutions, we obtain numerically the dispersion relations of the first few modes in the low-, intermediate-and high-wavenumber regimes, and we analyzed the eikonal limit.