Time-Dependent Supersymmetric Solutions in M-Theory and the Compactification-Decompactification Transition

We show that the diagonal light-like solution with 16 supersymmetries in eleven-dimensional supergravity derived in our previous paper (hep-th/0509173) can be generalised to non-diagonal solutions preserving the same number of supersymmetries. This class of solutions contains a subclass equivalent to the class of solutions found by Bin Chen that are dependent on the spatial-coordinates. Utilising these solutions, we construct toroidally compactified solutions that smoothly connect a static compactified region with a dynamically decompactifying region along a null hypersurface.