Astronomy and Astrophysics – Astronomy
Scientific paper
May 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988mnras.232..259f&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 232, May 15, 1988, p. 259-275.
Astronomy and Astrophysics
Astronomy
20
Relativistic Effects, Stellar Oscillations, Eigenvectors, Newton Theory, Relativity, Sturm-Liouville Theory
Scientific paper
Much that is known about the general pulsational properties of non-rotating Newtonian stars is traceable to the fact that in the Cowling approximation, the stellar pulsation equations can be cast in a nearly Sturm-Liouville form. In this paper, the relativistic Cowling approximation (an approximation scheme first introduced by McDermott, Van Horn and Scholl and analogous to the Newtonian Cowling approximation) is investigated, and it is shown that in this approximation the equations for non-radial relativistic stellar pulsations are also of nearly Sturm-Liouville character. The consequences of this are discussed as a series of theorems regarding the eigenfrequencies and eigenfunctions of g-, f- and p-modes in relativistic stars.
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