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 can be generalised to non-diagonal solutions preserving the same number of supersymmetries. Although the metric coefficients of this generalised light-like solution depend on only a single null coordinate, 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. (author)