The traditional approximation in general relativity

Abstract

We discuss the generalisation of the so-called traditional approximation, well known in geophysics, to general relativity. We show that the approximation is applicable for rotating relativistic stars provided that one focuses on relatively thin radial shells. This means that the framework can be used to study waves in neutron star oceans. We demonstrate that, once the effects of the relativistic frame-dragging are accounted for, the angular problem reduces to Laplace's tidal equation. We derive the dispersion relation for various classes of waves in a neutron star ocean and show that the combined effects of the frame-dragging and the gravitational redshift typically lower the frequency of a mode by about 20%.