Note on the quasinormal modes with a large imaginary component - art. no. 063002

We make two remarks about the calculation of the large imaginary component of the quasinormal modes associated with a Schwarzschild black hole. First, we display an analytical approximation for the radial component of the Reg ge-Wheeler-Zerilli equation that yields, to the lowest order, the main asym ptotic value for the imaginary part of these quasinormal modes. The link be tween the boundary conditions and the value adopted by the quasinormal freq uency is transparent within this approximation. In a second part, we refer to the strategy followed by Nollert in his search of these modes. The quasi normal modes appear as the frequencies that avoid the divergence of a conti nued fraction. The terms from n = N to infinity, in this series, are replac ed for what is called the remainder R-N(omega). In searching these frequenc ies, Nollert assumed, without justification, an asymptotic approximation fo r R-N(omega). This step is of some relevance since it opened to him the pos sibility to compute, numerically, frequencies with a higher imaginary compo nent than previous attempts. Here, we display a simple argument that justif ies this procedure. We also show that our approach gives a dosed form for R -N. The approximation displayed in this note for the computation of the qua sinormal modes is straightforward. From our point of view, it reinforces th e confidence on the clever numerical approaches introduced lately in this r esearch area. [S0556-2821(99)01704-X].