We can associate a Newtonian model with purely gravitoelectric (). 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 (). The anti-Newtonian model obstructs sounding solutions. In Ref. , it has been proven that the anti-Newtonian model shall include either shear or vorticity.