Transformation Between the Schwarzschild Coordinates and Local Inertial Coordinates

Abstract: We present a transformation between the Schwarzschild coordinates and local inertial coordinates, and demonstrate the effect of gravitational bending of light near a massive body in a small region. When a photon is emitted from a point near the Earth's surface with an initial horizontal direction, its parabolic trajectory would have a vertical deflection that is about three times that of a non-relativistic Newtonian particle would trace.