Is Gravity Truly Balanced? A Historical-Critical Journey Through the Equivalence Principle and the Genesis of Spacetime Geometry

Abstract

We present a novel derivation of the spacetime metric generated by matter, without invoking Einstein's field equations. For static sources, the metric arises from a relativistic formulation of D'Alembert's principle, where the inertial force is treated as a real dynamical entity that exactly compensates gravity. This leads to a conformastatic metric whose geodesic equation, parametrized by proper time, reproduces the relativistic version of Newton's second law for free fall. To extend the description to moving matter, uniformly or otherwise, we apply a Lorentz transformation to the static metric. The resulting non static metric accounts for the motion of the sources and, remarkably, matches the weak field limit of general relativity as obtained from the linearized Einstein equations in the de Donder or Lorenz gauge. This approach, at least at Solar System scales, where gravitational fields are weak, is grounded in a new dynamical interpretation of the Equivalence Principle. It demonstrates how gravity can emerge from the relativistic structure of inertia, without postulating or solving Einstein's equations.