  Addressing a long-standing problem, we show that every van Stockum dust can
be matched to a 1-parametric family of non-static Papapetrou vacuum metrics,
and the converse. The boundary, if existing, is determined by vanishing of
certain first-order invariant on the vacuum side. Moreover, we establish a
relation to Ehlers and Kramer--Neugebauer transformations, which allows us to
look for dust clouds with a prescribed boundary. Explicit examples include the
Bonnor metric and a new vacuum exterior to the Lanczos--van Stockum dust
metric, as well as dust clouds with nontrivial topology.
