Anisotropic velocity of light in non-inertial reference frames

Up to now little attention has been paid to an expression for the velocity of light in a gravitational field derived by Einstein in 1911. It is shown that (i) this expression represents the proper velocity of light (since it is defined in terms of proper time and length), (ii) the proper velocity of light is anisotropic in non-inertial reference frames, and (iii) unlike the coordinate velocity of light (which is a function only of the gravitational potential of the point at which it is determined) the proper velocity of light depends on the difference of the gravitational potential of the source and observation points and is expressed in terms of the initial velocity with which a light signal is emitted at the source point. The proper velocity of light is of crucial importance for two reasons: (i) it is this velocity (not the coordinate velocity) that is involved in the verification of the equivalence principle by calculating the potential and the electric field of a charge in an accelerating reference frame N_a and in a frame N_g supported in a uniform gravitational field as well as the self-force acting on a charge in N_a and N_g on account of its own electric field, and (ii) the proper velocity of light demonstrates that the local velocity of light is not always c which contradicts the standard curved-spacetime interpretation of general relativity