Gravitational Acceleration of a Moving Object at the Earth’s Surface

Einstein deduced (very briefly on p. 834 of [1], and in slightly more detail on pp. 820-822 of [2]) that the gravitational deflection of light according to general relativity is twice the “Newtonian” value. Einstein did not deduce the acceleration of light (or that of other fastmoving particles), which has perhaps left the impression that the acceleration at the surface of the Earth is no different from that in Newton’s theory (because curvature of space occurs only over large distances in “outer space”). Indeed, the topic of the acceleration due to gravity in Einstein’s theory seems to be rarely discussed. It appears in somewhat disguised form in sec. VC of [7] (titled “Laboratory experiments to test relativistic gravity”), where I interpret eq. (6.18) as implying