Classical solutions of the equations of supergravity

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Abstract
We describe an algorithm to solve the classical equations of supergravity for the coupled fields of helicity 2 and 3/2. The algorithm depends on an expansion in the associated Grassman algebra and leads to a sequence of coupled equations that may be solved in a step by step manner. The procedure begins with solutions of the usual empty space Einstein equations but the subsequent equations are all linear differential equations. To complete the method, it is necessary to generalize the supplementary conditions on the vector spinor field from flat to curved space. The algorithm also permits a classification of the complete solutions in terms of the associated gravitational fields. It is shown that vanishing curvature implies Minkowski space and does not permit other conceivable possibilities such as a Clifford space. Generalizations of the vanishing curvature space are suggested.

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