Formulating the r-mode Problem for Slowly Rotating Neutron Stars

We revisit the problem of inertial r-modes in stratified stars, drawing on a more precise description of the
composition stratification in a mature neutron star. The results highlight issues with the traditional approach to the
problem, leading us to rethink the computational strategy for the r-modes of nonbarotropic neutron stars. We
outline two strategies for dealing with the problem. For moderate to slowly rotating neutron stars the only viable
alternative may be to approach the problem numerically from the outset, while a meaningful slow-rotation
calculation can be carried out for the fastest known spinning stars (which may be close to being driven unstable by
the emission of gravitational waves). We demonstrate that the latter approach leads to a problem close, but not
identical, to that for barotropic inertial modes. We also suggest that these reformulations of the problem likely
resolve the long-standing problem of singular behavior associated with a corotation point in rotating relativistic
neutron stars. This issue needs to be resolved in order to guide future gravitational-wave searches.