Einstein’s equivalence principle states that locally, gravitational effects are indistinguishable from acceleration. This suggests that gravity is not a conventional force in spacetime, but rather a manifestation of spacetime geometry.

General relativity replaces the Minkowski metric with a dynamical metric $g_{\mu\nu}(x)$. In curved spacetime, proper intervals are given by $$ds^2 = g_{\mu\nu}dx^\mu dx^\nu,$$ and free-fall trajectories are geodesics.

Special relativity remains valid locally in freely falling frames, but no single global inertial frame exists in a generic gravitational field. Tidal effects reveal curvature through relative accelerations.