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

The Tolman type 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.