A Geometric Construction of Solutions to 11D Supergravity

Necessary and sufficient conditions are provided for a class of warped product manifolds with non-vanishing flux to be supersymmetric solutions of 11D supergravity. Many non-compact, but complete solutions can be obtained in this manner, including the multi-membrane solution initially found by Duff and Stelle. In a different direction, an explicit 5-parameter moduli space of solutions to 11D supergravity is also constructed which can be viewed as non-supersymmetric deformations of the Duff–Stelle solution.