  Gompf's end-sum techniques are used to establish the existence of an infinity
of non-diffeomorphic manifolds, all having the same trivial ${\bf R^4}$
topology, but for which the exotic differentiable structure is confined to a
region which is spatially limited. Thus, the smoothness is standard outside of
a region which is topologically (but not smoothly) ${\bf B^3}\times {\bf R^1}$,
where ${\bf B^3}$ is the compact three ball. The exterior of this region is
diffeomorphic to standard ${\bf R^1}\times {\bf S^2}\times{\bf R^1}$. In a
space-time diagram, the confined exoticness sweeps out a world tube which, it
is conjectured, might act as a source for certain non-standard solutions to the
Einstein equations. It is shown that smooth Lorentz signature metrics can be
globally continued from ones given on appropriately defined regions, including
the exterior (standard) region. Similar constructs are provided for the
topology, ${\bf S^2}\times {\bf R^2}$ of the Kruskal form of the Schwarzschild
solution. This leads to conjectures on the existence of Einstein metrics which
are externally identical to standard black hole ones, but none of which can be
globally diffeomorphic to such standard objects. Certain aspects of the Cauchy
problem are also discussed in terms of ${\bf R^4_\Theta}$\models which are
``half-standard'', say for all $t<0,$ but for which $t$ cannot be globally
smooth.
