One way to explain the present acceleration of the universe is Einstein_s cosmological constant. It is quite likely, in view of some recent studies, that a time-dependent equation of state had caused the Universe to evolve from an earlier phantom-energy model. In that case, traversable wormholes could have formed spontaneously. It is shown in this paper that such wormholes would eventually have become black holes. This would provide a possible explanation for the huge number of black holes discovered, while any evidence for the existence of wormholes is entirely missing, even though wormholes are just as good, in terms of being a prediction of general relativity, as black holes.

Traversable
wormholes, whose possible existence was first conjectured by Morris and Thorne
in 1988 [

In this paper, we study an equation of state that is both space and time dependent. It is proposed that if the equation of state evolved into the present cosmological constant model, then any wormhole that had previously come into existence would have formed an event horizon, thereby becoming a black hole. This would provide a possible explanation for the failure to detect any evidence of wormholes, while black holes appear to be abundant.

Interest in
traversable wormholes has increased in recent years due to an unexpected
connection, the discovery that our Universe is undergoing an accelerated
expansion [

Another widely studied possibility is the case

Two recent papers [

It is shown in [

An earlier study [

Since the equation of state is time dependent, we
assume that the corresponding metric is also time dependent. It is shown in the
next section that such a metric describes a slowly evolving wormhole structure
without assigning specific functions to

Evolving wormhole geometries are also discussed in
[

Since we are dealing with a given time-dependent
equation of state, it is natural to consider the consequences of an evolving
equation, particularly one in which the parameter

In this paper,
we will be dealing with a time-dependent metric describing an evolving
wormhole

In view of line element (

Graph showing the qualitative features of

To obtain a traversable wormhole, the shape function
must obey the usual flare-out conditions at the throat, modified to accommodate
the time dependence

The next step is to list the time-dependent components
of the Einstein tensor in the orthonormal frame. (For a derivation, see
Kuhfittig [

Recall that from the Einstein field equations in the
orthonormal frame,

Since (

Since the notion of dark or phantom energy applies
only to a homogeneous distribution of matter in the Universe, while wormhole
spacetimes are necessarily inhomogeneous, we adopt the point of view in Sushkov
[

Given the evolving equation of state (

Returning to (

From the
Einstein field equations

The line element now becomes

As an illustration, if

At this point, the following remark is in order: since
we are only interested in the possible existence of wormholes, it is sufficient
to note that to complete the description, the wormhole material should be cut
off at some

As we have
seen, since

In this section, we study the consequences of our
assumption that

In (

In summary, this paper discusses a wormhole geometry
supported by a generalized form of phantom energy; the equation of state is