Complex Normal-mode Frequencies of External Perturbations in Generalized Schwarzschild Geometry

A modified Wentzel-Kramers-Brillouin approach is used to determine the complex normal-mode frequencies of external perturbations in generalized Schwarzschild geometry. In the λ = 1 case (Schwarzschild geometry), the agreement with other methods is excellent for the low-lying modes. On the contrary, the λ ≠ 1 case of this geometry is unstable against external perturbations.