5 Newtonian and Anti-Newtonian Fields

We can associate a Newtonian model with purely gravitoelectric ($H_{ab}=0$). Without the gravitomagnetism, the nonlocal nature of the Newtonian force cannot be retrieved from relativistic models. It also excludes gravitational waves. The Newtonian model is a limited model to show the characteristics of the gravitoelectric. We can also consider an anti-Newtonian model; a model with purely gravitomagnetic ($E_{ab}=0$). The anti-Newtonian model obstructs sounding solutions. In Ref. [43], it has been proven that the anti-Newtonian model shall include either shear or vorticity.