Relativistic stellar pulsations in the Cowling approximation

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 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. (author)