Model for the completeness of quasinormal modes of relativistic stellar oscillations

Relativistic stellar oscillations are fluid and metric perturbations characterized by complex frequencies called quasinormal modes. This Letter presents a model which clarifies the extent to which such modes can be complete, in the sense of normal modes. It is found, for a specific class of Cauchy data, that, describing purely outgoing radiation, an expansion of the dynamics in terms of quasinormal modes can be constructed. For more general Cauchy data, it is shown that no useful distinction is possible between data that do and do not stimulate quasinormal oscillations.