  A new method is presented here for evaluating approximately the pulsation
modes of relativistic stellar models. This approximation relies on the fact
that gravitational radiation influences these modes only on timescales that are
much longer than the basic hydrodynamic timescale of the system. This makes it
possible to impose the boundary conditions on the gravitational potentials at
the surface of the star rather than in the asymptotic wave zone of the
gravitational field. This approximation is tested here by predicting the
frequencies of the outgoing non-radial hydrodynamic modes of non-rotating
stars. The real parts of the frequencies are determined with an accuracy that
is better than our knowledge of the exact frequencies (about 0.01%) except in
the most relativistic models where it decreases to about 0.1%. The imaginary
parts of the frequencies are determined with an accuracy of approximately M/R,
where M is the mass and R is the radius of the star in question.
