system
Given the following post, respond as if you're commenting on Reddit:
human
What is the speed of light in a non-inertial frame of reference?

I recently watched a VSauce video where they said that light travels at a constant speed for everyone as long as you aren't accelerating. So what happens when you accelerate? Does the speed of light change, and if so how can we calculate the new speed?
gpt
This is the thing that is the case: if a beam of light moves past you in your immediate vicinity and you have the ability to measure its speed as it does so, then you will measure its speed to be c. 

That's really *it*. That's the only completely relativistically correct thing you can say about the speed of light. In general relativity there just isn't a concept of the speed of an object that's far away from you. Or, which is the same thing, there are a whole infinity of different concepts you could choose from to try to replace the intuitive pre-relativistic one and no strong reason to prefer one to the other. 

Speed is not a scalar in GR. It's only built out of the spatial components of the four velocity. So it is a coordinate dependent quantity. You can always choose coordinates that are *locally* Minkowski and see that the speed of light is c (via SR) for light in your "locale" (and therefore that you would measure it as such even if you decided to use other coordinates). But you cannot necessarily extend those coordinates any great distance from yourself so you can't apply the same argument to light that isn't moving right by you. The speed you would assign to distant light (or anything else) depends on which coordinates you choose and even on which paths you imagine moving your rules and stopwatches across the universe along to actually do the measurement. There's no one choice that could be regarded as canonical. So it's fair to say that the speed of a distant object just isn't a thing in GR. At least not without first choosing enough conventions. (Kinda how cosmologists have different conventions for distance--angular diameter distance, luminosity distance, etc. These would all be the same in a Newtonian universe (or even an SR universe), but not in reality.)