  In this paper we discuss a new approach to the quasinormal-mode problem in
general relativity. By combining a characteristic formulation of the
perturbation equations with the integration of a suitable phase-function for a
complex valued radial coordinate, we reformulate the standard outgoing-wave
boundary condition as a zero Dirichlet condition. This has a number of
important advantages over previous strategies. The characteristic formulation
permits coordinate compactification, which means that we can impose the
boundary condition at future null infinity. The phase function avoids
oscillatory behaviour in the solution, and the use of a complex radial variable
allows a clean distinction between out- and ingoing waves. We demonstrate that
the method is easy to implement, and that it leads to high precision numerical
results. Finally, we argue that the method should generalise to the important
problem of rapidly rotating neutron star spacetimes.
