We consider the stability of spatially homogeneous plane-wave spacetimes. We
carry out a full analysis for plane-wave spacetimes in (4+1) dimensions, and
find there are two cases to consider; what we call non-exceptional and
exceptional. In the non-exceptional case the plane waves are stable to
(spatially homogeneous) vacuum perturbations as well as a restricted set of
matter perturbations. In the exceptional case we always find an instability.
Also we consider the Milne universe in arbitrary dimensions and find it is also
stable provided the strong energy condition is satisfied. This implies that
there exists an open set of stable plane-wave solutions in arbitrary
dimensions.Comment: 15 pages, no figures; minor changes, new references, to appear in CQ
