Quark matter is believed to exist in the center of neutron stars. A combined model consisting of quark matter and ordinary matter is used to show that the extreme conditions existing in the center could result in a topology change, that is, in the formation of wormholes.

Wormholes are handles or tunnels in the spacetime topology connecting different parts of our universe or of different universes. The meticulous analysis in [

Also introduced in [

While Morris and Thorne concentrated on traversable wormholes suitable for humanoid travelers (and possible construction by an advanced civilization), a more general question is the possible existence of naturally occurring wormholes [

A class of exact solutions of the Einstein-Maxwell field equations describing a wormhole with an anisotropic matter distribution is discussed in [

A combined model consisting of neutron-star matter and of a phantom/ghost scalar field yielding a nontrivial topology is discussed in [

For our basic equations we follow [

The Einstein field equations are listed next [

In the MIT bag model, the matter equation of state is given by
^{3} [

Since we are assuming the pressure to be isotropic, the conservation equation is [

As noted in the Introduction, we will concentrate mainly on the noninteracting fluid model. This means that the two fluids, normal matter and quark matter, do not interact. The resulting conservation equations are therefore independent of each other. Using (

As noted in Section

To study the other requirement,

Unfortunately, the constants

To analyze (

Since we are now concerned with what is going to become the throat at ^{3} to ^{3}, we may take ^{3}. So in geometrized units,

The assumption

Next, given the enormous density near the center of a neutron star,

Finally, observe that the other factor in the denominator,

We conclude that

As we have seen,

Since the throat of the wormhole is deep inside the neutron star, it cannot be directly observed. According to [

The quark-matter core, being surrounded by nuclear matter, raises a question regarding the interface region. As noted in the Introduction, quark matter is believed to be weakly interacting. So the most likely result is a drop in the energy density in the neighborhood of the core's surface.

If quark matter is eliminated from the model, then the right-hand side of (

It now becomes apparent that our conclusion depends critically on the fact that

We conclude with some brief comments on the interacting case. If the two fluids are assumed to interact, then the conservation equations take on the following forms [

Quark matter is believed to exist in the center of neutron stars. The analysis in this paper is therefore based on a two-fluid model comprising ordinary and quark matter with an isotropic matter distribution. It is shown that the extreme conditions may result in a topology change; that is, for certain choices of the matter content in the Einstein field equations, a neutron star could give rise to a wormhole.