A Star Harbouring a Wormhole at its Core

We consider a configuration consisting of a wormhole filled by a perfect fluid. Such a model can be applied to describe stars as well as neutron stars with a nontrivial topology. The presence of a tunnel allows for motion of the fluid, including oscillations near the core of the system. Choosing the polytropic equation of state for the perfect fluid, we obtain static regular solutions. Based on these solutions, we consider small radial oscillations of the configuration and show that the solutions are stable with respect to linear perturbations in the external region.