The Newtonian model obstructs wave solution, due to the
instantaneous interaction. Following
Refs. [28,29,30], we consider a model
whose action propagates at infinite speed (
This is compatible with
arbitrary function of time.
We define the Newtonian potential as
On substituting into Eq. (65a), we get
In a spatial infinity, we obtain the Poisson equation of the
Equation (65a) generalizes the gravitoelectric as the
Newtonian force in the gradient of the relativistic energy density.
Moreover, Eq. (66a) gives
In the Newtonian theory, we could not find the temporal evolution of
the Newtonian potential.