  The Weyl curvature includes the Newtonian field and an additional field, the
so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci
identities to provide a set of constraints and propagations for the Weyl
fields. The temporal evolutions of propagations manifest explicit solutions of
gravitational waves. We see that models with purely Newtonian field are
inconsistent with relativistic models and obstruct sounding solutions.
Therefore, both fields are necessary for the nonlocal nature and radiative
solutions of gravitation.
