Comment on “Quasinormal modes in Schwarzschild–de Sitter spacetime: A simple derivation of the level spacing of the frequencies”

It is shown here that the extraction of quasinormal modes within the first Born approximation of the scattering amplitude is mathematically not well-founded. Indeed, the constraints on the existence of the scattering amplitude integral lead to inequalities for the imaginary parts of the quasinormal mode frequencies. For instance, in the Schwarzschild case, $0\le {\omega }_I<\kappa$ (where $\kappa$ is the surface gravity at the horizon) invalidates the poles deduced from the first Born approximation method, namely, ${\omega }_n=in\kappa$.