Gauge, Diffeomorphisms, Initial-Value Formulation, etc The Einstein equations and the large scale behavior of gravitational fields

We introduce a large class of systems of partial differential equations on a base manifold M, a class that, arguably, includes all systems of physical interest. We then give a general definition — applicable to any system in this class — of “having the diffeomorphisms onM as a gauge group”, and “having an initial-value formulation, up to this gauge”. This definition is algebraic in the coefficients of the differential equation. The Einstein system, of course, satisfies our definition. There do not, however, appear to be many other systems that do, suggesting that these properties are rather special to the Einstein system.