  A characterization of the foliation by spacelike slices of an
$(n+1)$-dimensional spatially closed Generalized Robertson-Walker spacetime is
given by means of studying a natural mean curvature type equation on spacelike
graphs. Under some natural assumptions, of physical or geometric nature, all
the entire solutions of such an equation are obtained. In particular, the case
of entire spacelike graphs in de Sitter spacetime is faced and completely
solved by means of a new application of a known integral formula.
