The geometry ofD= 11 null Killing spinors

We determine the necessary and sufficient conditions on the metric and thefour-form for the most general bosonic supersymmetric configurations of D=11supergravity which admit a null Killing spinor i.e. a Killing spinor which canbe used to construct a null Killing vector. This class covers allsupersymmetric time-dependent configurations and completes the classificationof the most general supersymmetric configurations initiated in hep-th/0212008.Comment: 30 pages, typos corrected, reference added, new solution included in section 5.1; uses JHEP3.cl