Timothy Clifton, Asta Heinesen, Oliver Pitt

The parameterized post-Newtonian (PPN) approach is the state of the art formalism for performing theory independent tests of weak-field gravity, and for constraining possible deviations from Einstein's theory. Within this framework, global conservation laws are useful for the calculation of dynamics and for giving meaning to parameters. In this paper we extend the concept of semi-conservative and fully-conservative theories of gravity to include situations in which compact astrophysical bodies are modeled as masses that are sensitive to their local environment, as relevant for theories that violate the strong equivalence principle. We find that globally conserved quantities can still exist in the presence of such sensitivities, and find their explicit forms when they do. We identify new ways of writing the coefficients that enter into the PPN metric when a theory of gravity admits conserved quantities in the presence of a sensitive body, and demonstrate the applicability of our approach by comparing it to known results in scalar-tensor theories of gravity.