On the non-radial oscillations of a star II. Further amplifications

Abstract

The two algorisms that one uses for determining the complex characteristic frequencies, σ = σ₀ + iσ_i, belonging to the quasi-normal modes of oscillations of a star, are shown to be equivalent. In the first algorism, one searches directly in the complex σ-plane to satisfy the requirement that at infinity there are only outgoing waves (and no incoming waves). In the second algorism, one restricts oneself to real σs and selects the solution with the minimum flux of gravitational radiation at infinity.