Propagation of electromagnetic waves in MOG: gravitational lensing

We investigate the solution of Maxwell's equations in curved spacetime within the framework of modified gravity (MOG). We show that besides the null-geodesic treatment of photons in MOG, using Maxwell's equations and covariant coupling with the extra vector sector of gravitation in MOG, we can extract the equation for the propagation of light. We obtain Fermat's potential and calculate the deflection angle of light during lensing from a point-like star. Our results show that the deflection angle obtained from the solution of the wave equation in MOG for the large-scale structures with larger impact parameter of light rays is proportional to that of general relativity (GR). For solar mass stars the deflection angle agrees with the prediction of GR. However, for the compact structures like the supermassive black hole Sagittarius A* at the centre of the Milky Way, the prediction for the deflection angle is larger than GR, which can be tested in future observations.