The core principle posits that gravity is not a force but a geometric feature where massive objects warp spacetime into curved manifolds described by Einstein's field equations. A free particle in this framework follows a geodesic, defined as the path of extremal proper time (maximum for timelike intervals), derived from minimizing an action proportional to world line length via the metric tensor and Christoffel symbols. This theory generalizes Newtonian mechanics within General Relativity by substituting flat Minkowski geometry with curved Riemannian geometry dependent on mass-energy distributions.
Prerequisite chain context: requires Rotational Symmetry and Coordinate Independence in Potentials.