Yvonne Choquet-Bruhat, The Cauchy Problem in Classical Supergravity Letters in Mathematical Physics 7 (1983) 459-467. 0377
Here is the quintessence of the article.
The article considers super fields valued in a “single, arbitrary, large enough” Grassmann algebra in the sense exposed in the book
Bryce de Witt, Supermanifolds, Cambridge Monographs on Mathematical Physics, 1984, 1992
In the following we shall not quite follow this, but make use of the observation that this really means that we are working over the sheaf topos on the site of superpoints, as described at super ∞-groupoid. This changes nothing about the actual computations and formulas, but somewhat strenghtens the conceptual background.
These are over each equations in . In degree 0 in the Grassmann generators this is just the ordinary Einstein equaitons of gravity for the 0-Grassmann degree component of the fields. This is a well defined and causal Cauchy problem.
The observation now is: the equations can be solved by induction over the total number of Grassmann generators. In each step, the problem is a well-defined causal Cauchy problem in a version of ordinary gravity coupled to a bunch of extra fields.