  It is well known that static wormhole configurations in general relativity
(GR) are possible only if matter threading the wormhole throat is
"exotic"---i.e., violates a number of energy conditions. For this reason, it is
impossible to construct {static} wormholes supported only by dust-like matter
which satisfies all usual energy conditions. However, this is not the case for
non-static configurations. In 1934, Tolman found a general solution describing
the evolution of a spherical dust shell in GR. In this particular case,
Tolman's solution describes the collapsing dust ball; the inner space--time
structure of the ball corresponds to the Friedmann universe filled by a dust.
In the present work we use the general Tolman's solution in order to construct
a dynamic spherically symmetric wormhole solution in GR with dust-like matter.
The solution constructed represents the collapsing dust ball with the inner
wormhole space--time structure. It is worth noting that, with the dust-like
matter, the ball is made of satisfies the usual energy conditions and cannot
prevent the collapse. We discuss in detail the properties of the collapsing
dust wormhole.
