The Tolman VII solution, trapped null orbits and w - modes

TL;DR

This paper investigates the Tolman VII solution, an exact model of neutron stars, revealing trapped null orbits and dominant axial w-mode potentials in certain regions, which has implications for gravitational wave physics.

Contribution

It demonstrates that the Tolman VII solution exhibits trapped null orbits and dominant axial w-mode potentials, providing new insights into neutron star oscillations and gravitational wave emission.

Findings

Trapped null orbits occur in the Tolman VII solution for certain radii.

The dynamical potential for axial w-modes can dominate over centrifugal effects.

Trapped null orbits are present even when the star's radius exceeds three times its mass.

Abstract

The Tolman VII solution is an exact static spherically symmetric perfect fluid solution of Einstein's equations that exhibits a surprisingly good approximation to a neutron star. We show that this solution exhibits trapped null orbits in a causal region even for a tenuity (total radius to mass ratio) $> 3$. In this region the dynamical part of the potential for axial w - modes dominates over the centrifugal part.