Parametrized post-Newtonian approximation and Rastall's gravitational field equations

Abstract

The parametrized post-Newtonian (PPN) approximation is generalized to accommodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield conserved energy-momentum and angularmomentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories.