Trapped gravitational wave modes in stars with R>3M

Abstract

The possibility of trapped modes of gravitational waves appearing in stars with R>3M is considered. It is shown that the restriction to R<3M in previous studies of trapped modes, using uniform density models, is not essential. Scattering potentials are computed for another family of analytic stellar models showing the appearance of a deep potential well for one model with R>3M. However, the provided example is unstable, although it has a more realistic equation of state in the sense that the sound velocity is finite. On the other hand it is also shown that for some stable models belonging to the same family but having R<3M, the well is significantly deeper than that of the uniform density stars. Whether there are physically realistic equations of state which allow stable configurations with trapped modes therefore remains an open problem.