Trapped gravitational wave modes in stars with R>3M

TL;DR

This paper investigates the existence of trapped gravitational wave modes in stars with radii greater than three times their mass, challenging previous assumptions and exploring the stability and potential of such modes in various stellar models.

Contribution

It demonstrates that trapped gravitational wave modes can exist in stars with R>3M using more realistic models, expanding the understanding beyond uniform density assumptions.

Findings

Deep potential wells can occur in models with R>3M.

Some models with R<3M have even deeper potential wells.

The stability of these configurations remains an open question.

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.