The strong equivalence principle from a gravitational gauge structure

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 Einstein's tensor theory and Nordström scalar theory for gravity but also suggests a way to implement a minimal violation of the strong equivalence principle.