Modos quase-normais de buracos negros plano-simétricos anti-de sitter em d dimensões

Abstract

Quasinormal modes of plane-symmetric anti-de Sitter (AdS) black holes in d spacetime dimensions are investigated. Following the gauge invariant prescription developed by Kodama, Ishibashi and Seto (2000), fundamental equations for gravitational perturbation in such a background are constructed. Within such a prescription, metric perturbations naturally split into three disjoint classes. Namely, tensor, vector and scalar perturbations. However, different gauge invariant quantities are chosen in the present work, because they are more suited to the particular boundary conditions usually imposed to find quasinormal modes in AdS spacetimes than those used by Kodama, Ishibashi and Seto. In particular, the quantities used here present also the so called hydrodynamic modes, i. e., shear modes for vector perturbations and sound wave modes for the scalar ones, what is not found using the former quantities. It is also shown that there is just one shear mode, which does not depend upon the number of spacetime dimensions (d). Moreover, it is also found a general expression for the sound wave modes in terms of the number of the parameter d for scalar perturbations, and that there is no such a hydrodynamic mode for the tensor sector. Horowitz-Hubeny power series method is used in numerical analysis to find the dispersion relations for the first few quasinormal modes, and also for the hydrodynamic modes. This analysis is performed for five and six spacetime dimensions in the case of tensor perturbations, and for four, five and six dimensions in the cases of vector and scalar perturbations. The dispersion relations of regular modes present the same general behavior for all kinds of perturbations, Re(w) → q and Im(w) → 0 in the limit q → ∞, where w and q are the normalized frequency and the normalized wave number, respectively.