Following observations of super-fluid liquids in some stars, theorics have wandered if they could actually be a part of a wormhole, connecting the star to an aparent other star

After the discovery of the accelerated expansion of the present Universe at the end of the 1990ies, a great deal of attention has focused on models in which violation of one of the energy conditions takes place. In hydrodynamical language, this means that the parameter w in the equation of state p = w, defining the ratio of the pressure p of some matter to its energy density, may be less than −1/3 (i.e. violation of the strong energy condition), or even less than −1 (i.e. violation of the weak energy or null energy condition). While w = −1 is realized by the presence of a cosmological constant, leading to exponential expansion of the Universe, w < −1 would be realized by phantom matter with a possible end of the Universe in a finite time. Recent astronomical observations indicate that such a possibility is not excluded.

On the other hand, when considering models of compact astrophysical objects, a violation of the weak/null energy condition leads to a possible existence of configurations with "non-trivial topology", meaning traversable wormholes.

At the present time, much work has been devoted to the study of various models of both microscopic and macroscopic wormholes. One of the possible variants of obtaining wormhole-like solutions consists in considering ghost scalar fields, i.e. scalar fields with the opposite sign in front of the kinetic energy term. The use of such fields allows, in some cases, to obtain an equation of state with w < −1, and thus to violate the weak/null energy condition.

Models with ghost scalar fields have been considered earlier. In particular, in the papers a ghost scalar field with a Mexican hat potential was investigated and it was found that this system had regular, stable solutions only for topologically non-trivial (wormhole-like) geometry as suggested in the traversable Lorentzian wormhole-theory

In the case of macroscopic wormholes, ghost fields can be used to create models of astrophysical objects which can serve as entrances to wormholes. From the point of view of a distant observer, such objects will be quite similar to the usual star-like configurations, but they will have some characteristic features. Moreover, in the presence of electric and/or magnetic charges there exist new possibilities to detect such objects via galactic and extragalactic observations.

However, it is also possible to imagine a situation where the concentration of exotic matter violating the weak/null energy condition is formed at the center of an otherwise ordinary star. This in turn then leads to the possibility of the creation of a tunnel – a wormhole whose throat is filled with ordinary (star) matter. Thus an ordinary star or a neutron star could harbour some exotic matter at its center providing a nontrivial wormhole topology. For a distant observer, such a star would very much look like an ordinary star. However, also some distinctions should be present.

For example:
1) One of the most striking differences is that instead of a single star two similar stars will be observed that are separated in space. These two stars are associated with the two mouths of the wormhole.
2) Due to the fact that matter inside such star can move freely through the tunnel, the presence of radial (including quasiperiodical) motion is possible. Thus one can estimate the energy associated with such motion.

Source: arXiv.org