  We study string theory in supersymmetric time-dependent backgrounds. In the
framework of general relativity, supersymmetry for spacetimes without flux
implies the existence of a covariantly constant null vector, and a relatively
simple form of the metric. As a result, the local nature of any such spacetime
can be easily understood. We show that we can view any such geometry as a
sequence of solutions to lower-dimensional Euclidean gravity. If we choose the
lower-dimensional solutions to degenerate at some light-cone time, we obtain
null singularities, which may be thought of as generalizations of the parabolic
orbifold singularity. We find that in string theory, many such null
singularities get repaired by $\alpha'$-corrections - in particular, by
worldsheet instantons. As a consequence, the resulting string theory solutions
do not suffer from any instability. Even though the CFT description of these
solutions is not always valid, they can still be well understood after taking
the effects of light D-branes into account; the breakdown of the worldsheet
conformal field theory is purely gauge-theoretic, not involving strong
gravitational effects.
