  Gravitational self-interactions are assumed to be determined by the covariant
derivative acting on the Riemann-Christoffel field strength. Once imposed on a
metric theory, this Yang-Mills gauge constraint extends the equality of
gravitational mass and inertial mass to compact bodies with non-negligible
gravitational binding energy. Applied to generalized Brans-Dicke theories, it
singles out one tensor theory and one scalar theory for gravity but also
suggests a way to implement a minimal violation of the strong equivalence
principle.
