  We construct states on the algebra of the Klein-Gordon field that minimize
the energy density in homogeneous and in inhomogeneous spacetimes, both with
compact Cauchy hypersurfaces. The energy density is measured by geodesic
observers and smeared over a spacelike slab of spacetime, entirely containing a
Cauchy hypersurface and extended in time. We further show that these states are
Hadamard states. The present construction generalizes the construction of
States of Low Energy in Robertson-Walker spacetimes presented by Olbermann
(2007).
