Possible modifications of the gravitational deflection of light

Abstract

We investigate possible modifications on the gravitational deflection of light. Two forms of deformation of the Schwarzschild spacetime are proposed. The first ansatz is a given Finslerian line element; it could be regarded as a weak quantum gravity effect on the Schwarzschild spacetime. Starting from this ansatz, we deduce the deflection angle of the light ray which passes a weak gravitational source. The second ansatz could be regarded as a quantum vacuum effect on the Schwarzschild spacetime. The deflection angle of the light ray which passes a weak gravitational source is deduced in this Riemannian spacetime. This vacuum effect may distinguish the mixed light rays in the absence of gravitational source by a ``spectroscope'' (the gravitational source). The solutions of the gravitational field equation in this Riemannian spacetime imply this issue.