Classification of supersymmetric spacetimes in eleven dimensions

We derive, for spacetimes admitting a Spin(7) structure, the general local bosonic solution of the Killing spinor equation of eleven dimensional supergravity. The metric, four form and Killing spinors are determined explicitly, up to an arbitrary eight-manifold of Spin(7) holonomy. It is sufficient to impose the Bianchi identity and one particular component of the four form field equation to ensure that the solution of the Killing spinor equation also satisfies all the field equations, and we give these conditions explicitly.