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PeterDonis said:

To be more precise: the global bending of light when passing close by a massive object, i.e., the angle between its incoming path at infinity, and its outgoing path at infinity, is twice what you would expect from a naive Newtonian calculation

To be more precise: the local path of light through an accelerating elevator is "bent" downwards by the same amount as you would expect from a naive Newtonian calculation.

Yes, I was in a bit of a rush - though I probably couldn't be that precise anymore anyways. (Was I ever? Probably not, not that it matters). But that's the essence of why I think the factor of 2 is not present in this case. Basically, a purely Newtonian calculation should be good enough to handle the problem and there's no factor of 2 in said calculation. One simply take the travel time of the light, and during that travel time use the Newtonian formula for how far the rocket moves in that time period - i.e. 1/2 a t^2, as long as the rocket isn't accelerating for too long. "Too long" would be a good fraction of a year at 1g. So - no more than a few days to keep below 1 percent of c.

There shouldn't be any issues with the relativity of simultaneity or other relativistic effects that I can think of in this Newtonian analysis. The time coordinate that's held constant for the path of light in the instantaneous inertial frame should also be a constant Rindler time coordinate T. (If I was going to make an error, not unh eard of, this is probably where it would be).

I am pretty sure that my take on the "extra" deflection of light would generate some arguments, which I probably won't respond to - but I'm inclined to give the argument anyway for whatever it's worth, even if I may not h ave the time to get into a long conversation about it.

I use a coordinate dependent analysis - the coordinates I use are the PPN coordinates. And in those coordinates, I attribute the "extra" deflection to the PPN parameter gamma. Which is described as being a measure of spatial curvature in those specific coordinates. (The concept of what part of space-time curvature is "spatial" is of course coordinate dependent, which is why I am specifying what coordinates I am using in my argument).

If one consults wiki - which I believe takes the same information from MTW) - the PPN paramter for the extra curvature of light, gamma is described as

wiki said:

\gamma How much space curvature ##g_{ij}## is produced by unit rest mass.

And the curvature of light is entirely determined by ##1+\gamma## in the PPN formalism. Because ##\gamma## is one in General relativity, we see that light deflects twice as much.

That's my argument for why I attribute the "extra" curvature of light around a massive object to "spatial curvature", where the decomposition of the space-time curvature into a spatial part is given by the specific conventions used to define the PPN coordinates.

This spatial curvature is simply lacking in the case of light on an accelerating rocket / Einstein elevator / Rindler coordinates. (Rindler coordinates are spatially flat). Thus, I would not expect an extra factor of 2 for the deflection of light.