On the non-radial oscillations of a star. IV. An application of the theory of Regge poles

Abstract

It is shown how the flow of energy in the form of gravitational radiation, through a star in non-radial oscillations, can be determined by a suitable adaptation of Regge's theory of potential scattering in the quantum theory. While the resonant scattering of axial gravitational waves can be treated by Regge's theory, essentially, in its original form, the treatment of the resonant scattering of polar gravitational waves requires a generalization of the theory beyond its standard range and the incorporation of a 'flux integral' derived from independent considerations. Illustrative examples of the applications of the theory are provided.