Quasinormal modes in generalized Nariai spacetimes

Abstract

The perturbations of fields with spin 0, 1/2, and 1 propagating in a higher-dimensional generalization of the charged Nariai spacetime are investigated. The boundary conditions leading to quasinormal modes are analyzed and the quasinormal frequencies are analytically obtained.

Spin-2 quasinormal modes in generalized Nariai spacetimes

“…Finally, in Sec. V we present some conclusions and, taking into account the results of a previous work of ours [33], we find a formula for the quasinormal spectrum of a perturbation with generic spin and mass in the higher-dimensional Nariai space considered here. In the brief Appendix A, we provide explicit expressions for the angular functions adopted as a basis in this work.…”

“…condition, the reader is referred to Ref. [33]. Thus, summing up, we have just proved that the spectrum of the degrees of freedom H − jn and H jn is the one given in Eq.…”

“…This boundary conditions is the appropriate one to attain a quasinormal mode at the generalized Nariai spacetime, see Ref. [33].…”

“…Thus, in general, the perturbations of mater fields can be analysed independently from the gravitational perturbation. In our previous work [33] we have considered quasinormal modes associated the matter fields of spin 0, 1/2, and 1 in the generalized Nariai spacetime. Now, in this paper, we will tackle perturbations on the spin 2 gravitational field.…”

“…The boundary conditions of the quasinormal modes will be posed at these surfaces, as discussed in Ref. [33], and the domain of interest will be r ∈ (−Λ −1/2 , Λ −1/2 ). In such domain one can use the tortoise coordinate x defined by r = Λ −1/2 tanh(xΛ 1/2 ), in terms of which the line element becomes…”