  We explore the well know mass deficit/surplus phenomenon in General
Relativity to suggest that it could play a part in the dark matter conundrum.
Specifically in collapses and condensations of matter associated with negative
intrinsic curvature of the foliation associated with the asymptotic boundary
conditions, the external (ADM) mass can vastly exceed the integrated local
energy over the internal volume. This can be phrased in terms of a deficit of
volume for a given surface area (with respect to zero curvature). We explore
the phenomenon in the context of generalizations of the Oppenheimer-Snyder
models and other "cut and paste" models, the Lemaitre-Bondi-Tolman metric and
several others. We produce constructions where the internal object is
contracting or expanding, has a life time different from the asymptotic
Universe, as well as a volume different than the escavated volume from the
Universe. These are purely relativistic constructions and they could play a
role in the puzzle of dark matter: attraction without visible or indeed any
matter.
