Gravitational Effects on Light Rays and Binary Pulsar Energy Loss in a Scalar Theory of Gravity

We summarize a scalar bimetric theory of gravity with a preferred reference frame. The dynamics are governed by an extension of Newton's second law. We recover geodesic motion together with Newton's attraction field in the static case and find Schwarzschild's metric in the static spherical case. We build asymptotic schemes of post-Newtonian (PN) and post-Minkowskian (PM) approximations, each based on associating a conceptual family of systems with the given system. At the 1PN approximation, there is no preferred-frame effect for photons, and we hence obtain the standard predictions of GR for photons. At the 0PM approximation, an isolated system loses energy by quadrupole radiation without any monopole or dipole term. Inserting this loss into the Newtonian two-body problem gives the Peters–Mathews coefficients of the theory.