Effects Of Proca Photon In Curved Spacetime

Examining the mass of the photon is a very important way to test "invariance of the velocity of light". For present methods to do this, based on Proca equation, more obvious effects would be obtained under longer experimental dimensions, especially astronomical background where experiments are possibly affected by gravitational fields. In this paper, an equation descriping Proca light traveling in gravitional field is derived. As applications of the equation, light deflection in spherically symmetric gravitational field and frequency shift of light traveling through plane gravitational waves. It is found that the effects made by gravitation is so small that can be ignored in observation.