  In the context of Bartnik's splitting conjecture, Galloway \cite{G}
conjectured that for any globally hyperbolic, spatially compact and future
timelike geodesically complete manifold $(M,g)$ satisfying the strong energy
condition, the future boundary of $(M,g)$ consists of one point. We show that
whereas this statement is true in dimension $2$ due to a result by Ehrlich and
Galloway \cite{EG}, it fails in every higher dimension, and that there are
plenty of counterexamples, more precisely: On a manifold of dimension $\geq 3$,
{\em every} globally hyperbolic conformal class contains future complete
metrics satisfying the strong energy condition.
