The local deflection of light

Abstract

We have derived the relationship between the radial proper distance, h, and the polar angle, phi, for a light ray that is emitted and travels in the neighborhood of the Earth's surface. General relativity predicts that, even locally, the equation which relates these two physical magnitudes differs from the one stated by the principle of equivalence. More precisely, we have proved that, in the weak field limit, the local physical trajectory, h=h(phi), is the one that would correspond to a massive Newtonian particle in a field two times greater. Therefore, and contrary to the generally accepted fact, the principle of equivalence gives only 1/2 part of the general relativity local deflection of light.