(IN)COMPLETENESS OF QUASINORMAL MODES

Abstract

A perturbed black hole emits radiation at certain characteristic frequencies, the quasinormal frequencies, similar to the spectrum of frequencies produced by a struck guitar string. The normal modes of a guitar string are complete, in the sense that any oscillation of the string may be written as a superposition of these modes. In the case of quasinormal modes, this is not the case in general. We present here a simple proof of this fact.