On the Metric Lorentz Invariant Newtonian Cosmology

We review a metric theory of gravitation that combines Newtonian gravity with Lorentz invariance. Beginning with a conformastatic metric justified by the Weak Equivalence Principle. We describe, within the Newtonian approximation, the spacetime geometry generated by a static distribution of dust matter. To extend this description to moving sources, we apply a Lorentz transformation to the static metric. This procedure yields, again within the Newtonian approximation, the metric associated with moving bodies. In doing so, we construct a gravitational framework that captures key relativistic features—such as covariance under Lorentz transformations—while remaining rooted in Newtonian dynamics. This approach offers an alternative route to describing weak-field gravitational interactions, without relying directly on Einstein’s field equations.