The relativity of spacetime and geometric relativistic dynamics

We apply Relativistic Newtonian Dynamics (RND), a Lagrangian-based, metric theory to a static, spherically symmetric gravitational field. Using a variational principle and conserved momenta, we construct several metrics, analytic everywhere except at r = 0, which have g(01) not equal 0 yet still leads to the same trajectories as in the Schwarzschild model. These metrics passes all classical test of GR. However, this model and GR predict different velocities on the trajectories, both for massive objects and massless particles. The total time for a radial round trip of light in RND is the same as in the Schwarzschild model, but RND allows for light rays to have different speeds propagating toward and away from the massive object. One of theses metrics keeps the speed of light toward the object to be c. We present possible experiments to test whether g(01)=0. RND extends to multiple non-static forces, each of which obeys an inverse square law and whose field propagates at the speed of light.