ABOUT THE SIGNIFICANCE OF QUASI-NORMAL MODES OF BLACK-HOLES

Quasinormal modes have played a prominent role in the discussion of pe rturbations of black holes, and the question arises whether they are a s significant as normal modes are for self-adjoint systems, such as ha rmonic oscillators. They can be significant in two ways: Individual mo des may dominate the time evolution of some perturbation, and a whole set of them could be used to completely describe this time evolution. It is known that quasinormal modes of black holes have the first prope rty, but not the second. It has recently been suggested that a discont inuity in the underlying system would make the corresponding set of qu asinormal modes complete. We therefore turn the Regge-Wheeler potentia l, which describes perturbations of Schwarzschild black holes, into a series of step potentials, hoping to obtain a set of quasinormal modes which shows both of the above properties. This hope proves to be futi le, though: The resulting set of modes appears to be complete, but it no longer contains any individual mode which is directly obvious in th e time evolution of initial data. Even worse, the quasinormal frequenc ies obtained in this way seem to be extremely sensitive to very small changes in the underlying potential. The question arises whether, and how, it is possible to make any definite statements about the signific ance of quasinormal modes of black holes at all, and whether it could be possible to obtain a set of quasinormal modes with the desired prop erties in another way.