Open AccessThe traditional approximation in general relativity
Author(s) -
Maniopoulou Asimina,
Andersson Nils
Publication year - 2004
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2004.07872.x
Subject(s) - physics , neutron star , general relativity , gravitational wave , gravitational redshift , dispersion relation , classical mechanics , theory of relativity , doubly special relativity , generalization , redshift , two body problem in general relativity , numerical relativity , astrophysics , introduction to the mathematics of general relativity , mathematical analysis , quantum mechanics , galaxy , mathematics
We discuss the generalization 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 per cent.