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

We show that the diagonal light-like solution with 16 supersymmetries ineleven-dimensional supergravity derived in our previous paper (hep-th/0509173)can be generalised to non-diagonal solutions preserving the same number ofsupersymmetries. This class of solutions contains a subclass equivalent to theclass of solutions found by Bin Chen that are dependent on thespatial-coordinates. Utilising these solutions, we construct toroidallycompactified solutions that smoothly connect a static compactified region witha dynamically decompactifying region along a null hypersurface.Comment: 28 pages, 3 figures; the published versio